Questions on Algebra: Exponents and operations on exponents answered by real tutors!

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Question 752368: why does (x+y)^0 equal 1? isn't 1+1?
Found 2 solutions by josgarithmetic, stanbon:
Answer by josgarithmetic(1540)   (Show Source):
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LOOK at the pattern to any number raised to integers above and below zero including zero. When you see the rules of exponents, you understand , , , .

What does mean? It means .

What would be ?
How about ?
Let' keep going.
What is ?

One important rule about exponents is like this:
If m and n are integers, then .
You will plainly know that if m=n, then .

Answer by stanbon(57387)   (Show Source):
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why does (x+y)^0 equal 1? isn't 1+1?
-----
Answer:
x/x = 1 as long as x is not zero
----
x^1/x^1 = x^(1-1) = x^0
------
Therefore x/x = 1 = x^0
============================
Now "x" can be anything.
It could be "(x+y}"
So (x+y)/(x+y) = 1 = (x+y)^0
==================================
Note: (x+y) cannot be zero.
==================================
Cheers,
Stan H.
============

Question 752348: I need step by step
This is the expression

a= 3 b= -7 b has to be shown as a negative number
Answer by josgarithmetic(1540)   (Show Source):
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This only requires knowing order of operations. The confusion I find is in how you arranged your rendering tags.

I will assume you mean this:

Parentheses first.
Just as you have,

EXPONENTS.

MULTIPLICATIONS AND DIVISIONS.

And you can finish...?

Question 752331: 3(x-2)(x+3)=
Answer by jim_thompson5910(28598)   (Show Source):
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3(x-2)(x+3)

3(x(x+3)-2(x+3))

3(x^2+3x-2x-6)

3x^2+9x-6x-18

3x^2+3x-18

Final Answer: 3x^2+3x-18

Question 752316: Solve
a) 2^(z-3) = 1/16
Can you please help me out? Thanks so much in advance:)
Can you please show the steps it would really help me understand:)
Answer by ankor@dixie-net.com(15660)   (Show Source):
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We can write 1/16 as a power of 2 also

If the numbers are equal, the exponents are equal, therefore:
z - 3 = -4
z = -4 + 3
z = -1
:
:
Check this: which is 1/16

Question 752002: having trouble understanding my math problems:
(2yz)^2(xyz)-2
3(x^2y^2)(3x^2y^2)-1
please help.
Thank you
Alexis 6th grade
Answer by josgarithmetic(1540)   (Show Source):
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(2yz)^2(xyz)-2

When the site's triple bracket tags are placed, the expression looks like

The exponent 2 applies to everything inside the grouping symbols.

The other grouped expression is not exponentiated but is present as a factor, so this means show the resulting multiplication:

because factors in a product can be legally moved to different positions within that product

ANSWER: and that is as far as you can do with it.

Question 751976: x 3/5
x 1/10
Answer by tommyt3rd(608)   (Show Source):
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please repost to include directions (what needs to be done to/with these expressions) :)

Question 751565: x^5/2=32
Answer by lwsshak3(6522)   (Show Source):
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x^5/2=32
raise both sides to the (2/5) power.
x=32^2/5
x=4 (5th root of 32=2(squared)=4)

Question 751519: hi,
how can i rearrange y=6-x-2*x^2 into parabola equation?
Answer by josgarithmetic(1540)   (Show Source):
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It already is an equation of a parabola. Are you wishing for standard form? Are you hoping to put into general form?

You have .
You can complete the square to process the equation into standard form so you might easily graph the parabola.

You would add and subtract something.

You need to use .

The trinomial part is grouped specifically because that part can be factored; being a square trinomial.
..
Continue to simplify.

Question 750794: A rubber ball rebounds to 85% of the height from which it is dropped.
a. How high is the first bounce if the ball is dropped from a height of 200 cm?
Answer by timvanswearingen(106)   (Show Source):
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Question 736402: Simplify: x to the power of one eleventh multiplied by x to the power of one fifth
Answer by tommyt3rd(608)   (Show Source):
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Question 736118: Simplify the expression. Assume that the variables represent non-zero numbers:
-7r^4(r^4)^3
Answer by tommyt3rd(608)   (Show Source):
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Question 750542: Please help...
A family refers to a group of two or more people related by birth. Marriage or adoption who resides together. In 2000, in Country A, the average family net worth was $360,000, and there were about 9.4x10^7 families. Calculate the total family net worth in Country A in 2000.
Answer by josmiceli(9697)   (Show Source):
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dollars

Question 750483: multiply this problem
(2a+2)^3=
Answer by jim_thompson5910(28598)   (Show Source):
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(2a+2)^3 = (2a+2)(2a+2)(2a+2)

(2a+2)^3 = (2a+2)(4a^2 + 8a + 4)

(2a+2)^3 = 2a(4a^2 + 8a + 4) + 2(4a^2 + 8a + 4)

(2a+2)^3 = 8a^3 + 16a^2 + 8a + 8a^2 + 16a + 8

(2a+2)^3 = 8a^3 + 24a^2 + 24a + 8

Question 750183: Write the expression with positive exponents only. Then simplify, if possible.
4-3
Answer by Alan3354(30993)   (Show Source):
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Write the expression with positive exponents only. Then simplify, if possible.
4-3
=========
No exponents are shown.
Use ^ (Shift 6) for exponents.
eg, x^2 is x squared

Question 750056: What is the inverse of +25 and how do you arrive at the answer? Thanks
Answer by josgarithmetic(1540)   (Show Source):
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What kind of inverse? Are you looking for (+25)*I=1, or are you looking for (+25)+I=0 ?

Question 750041: what is the value of 2^3^2^3^2
Answer by tommyt3rd(608)   (Show Source):
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As an integer the number of digits is essentially unlistable by a person. Try it on a software package

:)

Question 749897: 5/6x^(-1/4)
Answer by Alan3354(30993)   (Show Source):
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5/6x^(-1/4)
--------------
Do you have a question?

Question 749708: x to the 4th divided by x to the 5th power
Answer by lenny460(778)   (Show Source):
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x to the 4th divided by x to the 5th power.

x^4 / x^5 = 1/x

Answer:
1/x

Lennox Obuong
Algebra Tutor
Nairobi, Kenya
Email: obuong3@aol.com

Question 749592: How would I convert 523,000,000 to scientific notation?
Thanks :)
Answer by Alan3354(30993)   (Show Source):
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How would I convert 523,000,000 to scientific notation?
----------
= 5.23*10^s s = some exponent
Count how many places to move the decimal point to between the 5 and the 2.
That's the exponent s

Question 749132: I have tried this 100 times and have no idea what I am doing wrong. Simplify
3
-^ -4 did I write that correctly?
4
Thanks for any help
Answer by solver91311(16897)   (Show Source):
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It looks like you mean

If I interpreted your input correctly, then the correct way to render this expression in plain text is:

(3/4)^(-4)

A negative exponent indicates the reciprocal, so:

Then use

The rest is calculator work

By the way...100 times? Really? Show me three different tries.

John

Egw to Beta kai to Sigma
My calculator said it, I believe it, that settles it

Question 749119: (x^-1+y^-1)^-1
I am unsure of how I am supposed to finish this problem. I flipped it becaues of the negative exponent and ended up with x^-1+y^-1/1 and then flipped it again because of the negative exponents on x and y. And ended up with 1/2x and 1/2y. I Don't recall in our lesson seeing problems with negative exponents on the inside and outside so I just figured you would keep flipping them til they were gone. I have a feeling that is incorrect.
Answer by josgarithmetic(1540)   (Show Source):
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At the lower level, focus on the main denominator. Lowest Common Denominator of the main denominator is xy. Try this: Multiply the whole complex fraction by . That should give you something which simplifies neatly into a noncomplex fraction.

Question 748834: I just can't figure out this homework problem. Here it is
The numerator is the following (2.7π(2.5x10^4)^3) The denominator is 5^ -3 and the entire formula is in brackets to the power of 2
I'm going to write it in words because the preview looks a little off.
The numerator is (2.7 times Pi(2.5 times ten to the 4th)3rd power) The denominator is 5 to the negative 3rd power. The entire fraction is squared
I keep coming up with "in scientific notation" 2.8x10^30 and the answer should be 2.7x10^32
Thanks for any help
Answer by MathLover1(6638)   (Show Source):
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............

so, your solution is correct

Question 748714: Can someone help me with this one?
I hope I write this out right...
(-3*10^-3) (2*10^2)=
I think I have some of it. I get to -6*1-^-5= (and then I am lost - if that is even right) Can someone show me how to do this. My text book is useless in explanations. Thanks!
Found 2 solutions by rothauserc, stanbon:
Answer by rothauserc(210)   (Show Source):
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we are asked to evaluate
(-3*10^-3) (2*10^2)= (-3/10^3) * (2*10^2) note that 10^-3 = 1/10^3
= (-3/10) * (2) cancel 10^2 from numerator and denominator
= -6/10
= -3/5

Answer by stanbon(57387)   (Show Source):
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(-3*10^-3) (2*10^2)
--------
= -3*2*10^-3*10^2
--------
= -6*10^-1
----
= -6/10
----
= -0.6
============
Cheers,
Stan H.
============

Question 748291: 6m to the second power + 10m
This is factoring with greatest common factors
also help with these.
14d(little 3)-28d
20abc+15a(little 2)c - 10 ac
14h(little 3) - 24h(little 5)- 49h(little 4)
2ky(little 2) + 10k(little 3) y(little 2)
4x(little 2)y - 6xy(little 2)
12v(little 3) w(little 3) - 18v(little 2) w(little 2) + 30v
-x(little 5)- 4x(little 4) + 23k(little 3) -x
Answer by Cromlix(353)   (Show Source):
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6m^2 + 10m = 2m(3m + 5)
14d^3 - 28d = 14d(d^2 - 2)
20abc + 15a^2c - 10ac = 5ac(4b + 3a - 2)
14h^3 - 24h^5 - 49h^4 = h^3(14 - 24h^2- 49h)
2ky^2 + 10k^3y^2 = 2ky^2(1 + 5k^2)
4x^2y - 6xy^2 = 2xy(2x - 3y)
12v^3w^3 - 18v^2w^2+ 30v = 6v(2v^2w^3 - 3vw^2 + 5)
-x^5 - 4x^4 + 23k^3 - x = -x(x^4 + 4x^3 + 23k^3)
Hope this helps

Question 748127: How to simplify: (8a^-1)^3(a^2)^-3
Answer by MathLover1(6638)   (Show Source):
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Question 746204: Solve (6xy^3) (4x^2 y^4)
Answer by kekegeter (57)   (Show Source):
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6xy^3*4x^2y^4
24x^1=2 y^3=4
24x^3y^7

Question 747024: We need help - badly.... 4 x 3 to the 4th power + 6.
thank you.
Answer by Alan3354(30993)   (Show Source):
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4 x 3 to the 4th power + 6.
-------
4*3^4 + 6
= 4*81 + 6
= 324 + 6
= 330

Question 746821: My problem is 3 over 5n to the ninth power to the second power. My question is . Since the entire problem is raised to the second power, in the denominator, do i raise 5 to the second power or do ijust do 5 times 2
Answer by ankor@dixie-net.com(15660)   (Show Source):
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problem is 3 over 5n to the ninth power to the second power.
Assume the problem is:
= =

Question 746991: 3x^3(5x^2+2y)=
Answer by jim_thompson5910(28598)   (Show Source):
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3x^3(5x^2+2y)

3x^3(5x^2)+3x^3(2y)

15x^5+6x^3y

Final Answer: 15x^5+6x^3y

Question 736828: 7 raised to 5x-8 and 5 raised to x+2 if product of these two is equal to 30625 then how to find value of x

Answer by tommyt3rd(608)   (Show Source):
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:)

Question 743178: Please help me solve this.
Saying that 4 < sqrt(x) < 9 is equivalent to saying what about x?
Answer by tommyt3rd(608)   (Show Source):
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typically we want to write inequalities in terms of a variable, so we rewrite it in terms of just x:

:)

Question 742957: simplify the following. Do not leave any negitives. I do not understand how to get rid of the negitive, thank you for your help.
1
________
5^-2
Answer by tommyt3rd(608)   (Show Source):
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taking reciprocals reverses the sign on exponents:

so the result is 25

Question 746607: If you are solving the equation for 5 to the exponent of -2n=125 what would be the answer for that?
Answer by reviewermath(534)   (Show Source):
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, equate the exponents because the bases are now equal
-2n = 3

Question 746425: Express using a single radical, 16^(1/8)
Found 2 solutions by josgarithmetic, stanbon:
Answer by josgarithmetic(1540)   (Show Source):
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=
=

Answer by stanbon(57387)   (Show Source):
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Express using a single radical, 16^(1/8)
--------
8th root of 16
=================
Cheers,
Stan H.
===============

Question 745666: how do you do 9 to the 12th power full multiplication and long division

Answer by Alan3354(30993)   (Show Source):
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duplicate

Question 745667: how do you do 9 to the 12th power full multiplication and long division

Answer by Alan3354(30993)   (Show Source):
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how do you do 9 to the 12th power full multiplication and long division
-----------------
What do you mean by "do?"

Question 744998: Please Help me with this problem its all one problem all together
1) factor

Answer by josgarithmetic(1540)   (Show Source):
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The only part left undone is the 2 and the 8.

Question 744995: please help me solve (-0.4)^3
Answer by algebrahouse.com(1079)   (Show Source):
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(-0.4)³
= (-0.4)(-0.4)(-0.4) {took (-0.4) to the third power}
= -0.064 {multiplied}
www.algebrahouse.com

Question 744804: 5^2 and (3i)^2 what would this result in
Answer by savvyhush23(50)   (Show Source):
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what do you mean by "and", is it multiplication?
anyway, just to give you idea the imaginary "i" is equal to .
following your question, assuming "and" here is multiplication, then is equal to -225

Question 744687: what is the best way to explain to a 7th grader how to convert degrees farnheit to celcius?? and vice versa?
Answer by erika514(38)   (Show Source):
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Hi,
To convert degrees Fahrenheit to Celsius and Celsius to Fahrenheit, here are the formulas.

Conversion Formulas
--------------------------------------------------------------------------------

Fahrenheit to Celsius:
C = (F - 32) * 5/9

Celsius to Fahrenheit:
F = C * 9/5 + 32

To convert, plug in the given temperature in degrees Fahrenheit in for F, and subtract from 32, then multiply your difference by 5/9 to get the temperature in degrees Celsius. For a given Celsius temperature, plug in the value for c, multiply it by 9/5 and add 32 to get the temperature in degrees Fahrenheit. I would highly suggest using a calculator if possible to make work a lot easier.
Good luck and hope this helps! Let me know if you have any more questions. :)

Question 744665: Please help me solve this math problem 5/6-(1/11-1/8)
Answer by MathLover1(6638)   (Show Source):
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....first do

Question 744143: Please help me solve this equation: simplify
Answer by KMST(1874)   (Show Source):
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Take out common factor a.
Simplify, cancelling a's.
Recognize and use difference of squares special products
Factors in numerators and denominator cancel out.
Recognize square of binomial

--> (It's the minimum of the function)
If you know about hyperbolic functions, you may write the last equation as
<-->