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

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(1)
or
multiply each side by
divide each side by w
take the square root of each side


(2)
or
multiply each side by 10
take square root of each side


Does this help??----ptaylor

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You divide the 15 by 10 and you multiply the 10^6 by 10.
---------------------
You do this because scientific notation (ax10^b) requires that
0 So you can't just leave the answer as 15*10^6
--------------------------------
Cheers,
Stan H.

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8X10 (-9 exponent)
IS EQUAL TO 2X10 (-12 exponent) and is also EQUAL TO 0.000000000002
4X10 (3 exponent)
---------------
Comment: Where do you get these numbers. What you post
as being equal are not equal.
---------------
8x10^-9 = 0.000000008
2x10^-12 = 0.000000000002
4x10^3 = 4000
======================
Cheers,
Stan H.

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(4X10 ) X (7X10 = 28X10 - 2.8X10 =0.00028
?
-----------------------
(4X10) X (7X10)
= 28x10^2
Divide the 28 by 10 and multiply the 10^2 by 10.
= (2.8/10)x((7x10^2)x10)
= 2.8x10^3
===============
Cheers,
Stan H.

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Think about it.
You're dividing a large number (60000) by a much smaller number less than 1 (0.00002).
You will get an even larger number.
As an example:

.
.
.
Let's go through it step-by-step,

The rule of dividing exponential expressions is,





.
.
.
Similarly.

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I don't have the book, so I can't.

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8+4-3=12-3=9 ans.

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What is the expression of a^3b^2 over a^2b
------------------
It's
It can be reduced, a popular classroom activity.
Cancel a^2 and b
= ab

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what is the illegal values of b in the fraction 2b^2+3b-10 over b^2-2b-8?
:
The value for b which results in 0 in the denominator, to find that solve for b:
b^2 - 2b - 8 = 0
Factor
(b-4)(b+2) = 0
Two solutions
b = 4
b = -2
These are the illegal values for b, substitute these values for b in the denominator to see that we have division by 0 for these values

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What are the "illegal" values of b in the fraction:

The "illegal" (sometimes called "excluded") values of b are those values of b that would make the denominator equal zero. So, we set the denominator equal to zero and solve for b.
Solve by factoring.
Apply the zero product rule.
or , so that...
or These are the "illegal" values of b.

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we need the equations regarding x in order to answer these problems....please relist with the equations involving x.....thanks

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x^2-2x-3=0
(x-3)(x+1)=0 [factor]
x-3=0 [set each factor equal to zero and solve for the x-value]
x=3
and
x+1=0
x=-1
So, the solutions are x = 3 and x = -1

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Start with the given equation.


Notice we have a quadratic equation in the form of where , , and


Let's use the quadratic formula to solve for x


Start with the quadratic formula


Plug in , , and


Negate to get .


Square to get .


Multiply to get


Rewrite as


Add to to get


Multiply and to get .


Take the square root of to get .


or Break up the expression.


or Combine like terms.


or Simplify.


So the answers are or

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(3u^-4x^-9z^-5x^9)(4u^-7*5z^8)
(3x^9)/(u^4x^9z^5)(4*5z^8)/u^7
(3x^9)(20z^8)/(u^4x^9z^5)(u^7)
(60x^9z^8)/(u^11x^9z^5)
(60x^[9-9]z^[8-5])/u^11
(60x^0z^3)/u^11
60z^3/u^11 ans.

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2A/3 = 8 + 4A
(3) ( = ) [eliminate the fraction by multiplying completely by "3"]
.
2A = 24 + 12A [Isolate the "A" term if possible]
.
2A - 12A = 24 [Simplify]
.
-10A = 24
.
( = )

.
A=-2.4

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-7q^14x^[?]u^14/11q^14x^12u^3
HAVE YOU LEFT OUT A POWER TERM [ ] FOR X IN THE NUMERATOR?
IF YES. PLEASE RESUBMIT.

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What does the n represent in this question?

Can you be more specific?

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1. Find the equation of the line that passes through the points (-4,-11)
and(-2,-3).
|x y 1|
|-4 -11 1| = 0
|-2 -3 1|
x*(-11+3) -y*(-4+2) + 12-22 = 0
-8x +2y = 10
4x - y = -5
---------------
2. find the slope of the line containing the given points. P1(3,11), P2(6,17)
slope, m, = (diff in y)/(diff in x)
m = (17-11)/(6-3)
m = 2
----------------
Multiply
3. (x^2-7x+5)(3x-3) = 3x^3 - 24x^2 +36x - 15
------------
4. 6x^10-3x^8+1/x^4 = 6x^6 - 3x^4 + 1/x^4

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To remove the big parentheses, multiply
each of the six exponents inside the
parentheses, top and bottom, by the outer
exponent .





Move the factors with negative exponents in
the top to the bottom, changing the signs of
the negative exponents to positive. Also,
move the factors with negative exponents in
the bottom to the top, changing the signs of
the negative exponents to positive.



Add the exponents of x in the top 
Add the exponents of y in the bottom 
Write  as 




That may be acceptable as the final answer.

However we can rationalize the denominator by
multiplying top and bottom by 



Write the factors in the top
as radicals. Add exponents on 
the bottom.



Multiply under the radicals
and simplify the exponent in the
bottom:




Edwin

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yes

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3^(-2) = 1/(3^2)
Since 3^2 = 9,the final answer is: 1/9

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2a to the negative 3rd power b to the 1st power if a= 2 and b= 12
Do you mean 2a^(-3)(b^1)?
If so, here is the solution:
Replace a with 2 and b with 12
2(2)^(-3) (12^1))
2(1/8)(12)
(1/4)(12) = 3

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in an exponential expression such as A=b*e^-(t/RC) power, we cannot attach units to the exponent -(t/RC) because a base, such as e, can only be raised to a pure number. consequently, if the variable t in this equation is measured in seconds, what does this imply about the units on the product RC?
---------------------------
RC must also be in seconds so the units cancel leaving t/RC a pure number.
========================
Cheers,
Stan H.

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meters = (what?) * seconds?

meters per second means , so

. must be measured in meters per second.

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The same way you would solve any quadratic.

First put it in standard form:

Fortunately, this one factors because and , so



=>
or
=>

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How do you solve for y in the equation (y^2=y+30)?
------------
y^2=y+30 Get the zero on the right side
y^2 - y - 30 = 0
(y-6)*(y+5) = 0
One of the binomials has to be zero if the product is zero.
y = 6
y = -5

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g^-5.g^8
IF THIS IS A MULTIPLICATION PROBLEM THEN:
G^8/G^5=G^3 ans.

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y=-2x
-2x=y
x=y/-2 ans.

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1a...(2(-4))^3=(-8)^3=
:
b....(-3)(-4)^2(3-(3)(-4))=(-3)(16)(15)=
:
c....-(3)-(-4)^2-5=-3-16-5=
:
d....-2((3)(-4))^2=-2(144)=
:
2.a...-5w+9x-8w-4x.....so add the w terms and x terms together
........
b......-4+5y-3+5y+4y......combine y terms and constant terms
......

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1. Evaluate for a = 3 and b = -4
a) = =
b) ==
c) =
d) ==
2. Combine like-terms.
a) =
b) =

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8r²=76r
So? Do you have a question?

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How do you evaluate the expression
10^log(3.14)
Let x = 10^log(3.14)
Take the log to get
log(x) = log(3.14)*log10
log(x) = log(3.14)
x = 3.14
===============
In general 10^log(a) = a
===============
Cheers,
Stan H.

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rewrite the expression so that all exponents are positive
4d(to the negative 4) time e(to the negative 1) divided by f(to the -8)
------------------------------------
[4d^-4 * e^-1] / f^-8
= 4f^8 / [d^4*e]
======================
Cheers,
Stan H.

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F(5)=Y^3-2Y^2+3Y-4
F(5)=5^3-2*5^2+3*5-4 [HERE YOU MUST FIRST RAISE TO THE POWER (5^2) THEN MULTIPLY
F(5)=125-2*25+15-4
F(5)=125-50+15-4
F(5)=86 ANS.

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Let's write the equation

Using the power of powers rule, that yields

Now, 7*7 = 49
49*7 = 343
343*7 = 2401
2401 * 7 = 16807
Look at the ones digit above. You can see the pattern 7,9,3,1,7...
So the pattern repeats after each group of 4.
Thus 7^(4x+1) ends in 7
7^(4x+2) ends in 9
7^(4x+3) ends in 3
7^(4x+4) ends in 1
49/4 = 12.25 = (4*12) + 1
That means there are 12 groups of 4, plus one left over. That means you will be left with the ones digit ending in 7

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48a^3b^6c/12a^2b^4
[48/12=4]
[a^3/a^2=a^(3-2)=a^1=a]
[b^6/b^4=b^(6-4)=b^2]
4ab^2c ans.

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Looks OK to me.

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{3(7 - 9) + 16}^3 ÷ (-5) - 2^4
= (3(-2 + 16)^3/((-5) - 16) \\\ It's not clear what's meant to be in the denominator. Use more parentheses.
= (3*14)^3/(-21)
= 42^3/(-21)
= 42*42^2/(-21) A shortcut
= -2*42^2
= -3528

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(x^-3)^-2(x^-1y)^2/(xy^-2)^2
=(x^6)(x^-2y^2) / (x^2y^-4)
= (x^4y^2)/(x^2/y^4)
= x^2y^6
====================
Cheers,
Stan H.

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Put 1 exponents so everything will show an exponent:




First do this part: 
,
Then replace  by  



Inside the parentheses add exponents of a and of b:



Now we're ready to remove the parentheses by multiplying
every inner exponent top and bottom by the outer
exponent :





Move  from numerator to denominator and
change the sign of the exponent, and write 
on the bottom.
Likewise, move  from denominator to numerator and
change the sign of the exponent, and write 
on the top. 



Subtract exponents, larger minus smaller, and place the
result in the numerator or denominator, depending on
which one had the larger exponent before.

So we subtract exponents of a,  or 
and place this on the top since the exponent  was
larger than the exponent  and  was on the top.
We eliminate  from the bottom:



Finally we subtract exponents of b,  or 
and place this on the bottom since the exponent  was
larger than the exponent  and  was on the bottom.
We eliminate  from the top:



Edwin

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area of a rectangle equals length * width.
let A = area
let L = length
let W = width
A = L*W
-----
you are given the area and the width.
you want to find the length
-----
A = L*W
divide both sides of equation by W:
A/W = L
which is the same as:
L = A/W
-----
A = 15m^2 + 11m - 12
W = 5m-3
-----
substitute for A and W:
L = (15m^2 + 11m - 12) / (5m-3)
-----
this is a straight long division problem:
first you figure how many times 5m will divide into 15m^2.
answer is:
3m ********* this is the first part of your answer.
then you multiply (5m-3) * 3m
answer is:
(15m^2 - 9m)
then you subtract (15m^2 - 9m) from (15m^2 + 11m - 12)
answer is:
(15m^2 + 11m - 12) - (15m^2 - 9m) =
15m^2 + 11m - 12 - 15m^2 + 9m =
(20m - 12)
-----
next you figure out how many times 5m goes into 20m.
answer is:
4 ********* this is the second part of your answer
then you multiply (5m-3) * 4
answer is:
(20m - 12)
then you subtract (20m-12) from (20m - 12)
answer is:
20m - 12 - (20m - 12) =
20m - 12 - 20m + 12 =
0
-----
your answer for (15m^2 + 11m - 12) / (5m-3) is (3m + 4)
(3m+4) is the length.
-----
to prove your answer is correct, go back to the original equation of:
A = L*W
substitute for A, L, and W:
15m^2 + 11m - 12 = (3m+4)*(5m-3)
(3m+4)*(5m-3) = 15m^2 - 9m + 20m - 12 =
15m^2 + 11m - 12.
this is the same as the area you started with so the equation is true proving that the value of (3m+4) for the length is good.
-----
your answer is:
length = (3m+4)
-----

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15m2+11m-12
(5m-3)(3m+4)
3m+4 is the length.

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Divide - (x4-16) (x + 2)
----------------
Do you mean Divide (x4-16) by (x + 2) ?
That's

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Note:




and





In other words, we just flip the fractions


So

becomes






Distribute the exponents.


Multiply the exponents.


Subtract the exponents


For example,


Simplify


Combine the exponents.


Flip the variables with negative exponents.


Combine the fractions.


Simplify


==============================================

Answer:


So simplifies to


In other words, where no variables can be equal to zero.