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

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Question 994618: How do I helped a 6th grader learning numbers to power?...exmolesexamples: 2 to the third power; 5 to the fifth power; etc. What is the simple process for this grade level?
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The "power" is a normal counting number; so "third power" really means 3; "fifth power" really means 5. Those are telling the exponent to use on the (base) number.

means .

means .

Another example, ten to the second power is which is same as , which is the product, .

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Multiplication is a shortcut for expressing repeated addition of a number.
Exponentiation (at least using whole number exponents) is a shortcut for expressing multiplication of a repeated factor.

Question 994588: hello, i have a question with fractional exponents, (x^-1/7)/x, i have tried bringing the denominator x into the denominator making it X^-1/7x, after that i am stuck, i would like to write it in fractional exponents, thank you
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What you have is not well written. Maybe you have . That may render badly so is not readable, but if so, that is the best this system will do.

The exponent in the numerator on x is , and the exponent on x in the denominator is .

Those written steps, again, might not render but you can see the pure text in which they are written using the Show Source hyperlink on the page.

Question 994531: By completing the square, the expression x^2+2 x +92 equals (x+A)^2+B
Find A and B.

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The term to add and subtract is 1.

Also study these two lessons to help in learning more or better:

What is Completing the Square?
http://www.algebra.com/my/Completing-the-Square-Using-Pictures.lesson?content_action=show_dev
,
How to solve, but also includes HOW TO COMPLETE THE SQUARE

Question 994468: K9 power
Divided by
K5 power

Question 994342: 774+447+113 to base 8
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774+447+113 to base 8
------------
774
447
113
4+7+3 = 6 carry 1
7+4+1+1 = 5 carry 1
7+4+1+1 = 5 carry 1
--> 1556

Question 994049: What is the value of 0.3x to the 3rd power + 2
Found 2 solutions by Alex2dadeath, Boreal:
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0.3 to the third power or *cubed*.
SO the power is basically that number times itself that many times. (For instance, if I had 3 to the fourth power, it will be: 3x3x3x3).
So here, we got 0.3 x 0.3 x 0.3. ). 0.3 times 0.3 equals 0.09. Now multiply 0.09 with 0.3. You get 0.027.
Now you have to add 2. 2 is a full number with no decimal so do not add it to the right of the decimal. Add it to the 0 on the left of the decimal. 2 plus 0.027 equals 2.027.
0.027
+2.00
--------
2.027

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(0.3x)^3+2 is how I interpret the question.
0.027x^3+2
you cube 0.3
you cube x
=======
(0.3x+2)^3 is different. Start by squaring it.
0.09x^2+1.2x+4
Then multiply by 0.3x+2. There will be six terms:
0.27x^3+0.18x^2+0.36x^2+2.4x+1.2x+8
This is
0.27 x^3+0.54x^2+3.6x +8
=======
Notice the different results for the different interpretations of the problem.

Question 993994: 2^2x+1-15(2^x)=8
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=>
=> (Taking 2^x =y)
=>
=> or
=> or
=> x=3 (Since 2^x can not be negative.)

Question 993891: what is (h9j-4k4)3 equal? (btw the numbers are all exponents i just couldn't type them like that from my laptop)
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what is (h9j-4k4)3 equal?
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It's equal to what it says.
If you want to expand it:
Use ^ (Shift 6) for exponents.
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(h^9j - 4k^4)^3
For 3rd power, use the values from Pascal's triangle, 1 3 3 1
= (h^9j)^3 - 3*(h^9j)^2*(4k^4) + 3*(h^9j)*(4k^4)^2 - (4k^4)^3
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=
You might want to expand each term, I don't know.
email via the TY note for help or to check your work.

Question 993507: What is Y to the 2nd power times Y to the negative 5th power? Thank you!!
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y^2 * y^(-5) = y^(2 - 5) = y^(-3)

Question 993476: 3 to the 5 power X 5 to the 5th power

Question 993372: (4n) to the negative third power

Question 992950: x=y^4
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.
Very good.

Question 992957: How do you find the value of 3 by the 5th power?

Question 992914: (3a0 b-2)3 the 0 -2 and 3 are exponents
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(3a0 b-2)3 the 0 -2 and 3 are exponents
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= (3b-2)^3
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= (3b)^3 + 3(3b)^2(-2) + 3(3b)(-2)^2 + (-2)^3
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= 27b^3 - 54b^2 + 36b - 8
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Cheers,
Stan H.
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Question 992827: What is 14 to the 5 power divided by 14 to the negative 9 power. Thank you

Question 992828: How would I work out a binomial that looks like this q^2÷2q
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.
q^2 ÷ 2q = = = .

Question 992609: What is the smallest value of that statisfies , given that , , , , and are all positive integers, not necessarily different?
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What is the smallest value of +f+ that statisfies +a%5E2%2Bb%5E2%2Bc%5E2%2Bd%5E2=f%5E2+, given that +a+, +b+, +c+, +d+, +e+ and +f+ are all positive integers, not necessarily different?
:

Question 992616: How to evaluate (3/4)^-3
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(0.75)^-3=2.37
=2 37/100

Question 992617: How to evaluate (-2)^-4

Question 992541: 6 to 2nd power divided by 2(3) + 4 =
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.
What these mysterious symbols mean:

2(3) + 4 ???

Question 992495: An adult blue whale can eat 4.0 x 10^7 krill in a day. At that rate, how many krill can an adult blue what eat in 3.65 x 10^2 days? Please explain
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If you have a time to achieve a certain amount (such as a time to go a distance),
and a rate (such as a speed),
to find the amount you achieve (such as how far you can go) you multiply time and rate.
Of course, you have to mind your units, to match the units of time in your time and your rate
For example, to find how far you will go
driving 90minutes (1.5hours)
at 50 miles per hour, you multiply
.
In this case, to find how many krill that whale will eat in one year, you calculate
.
The factor 4.0 x 10^7 krill/day is given with 2 significant digits,
meaning that the rate is between 3.95 x 10^7 krill/day and 4.15 x 10^7 krill/day, and maybe your teacher would like you to show the answer with
as krill , meaning somewhere between krill and krill.

NOTE: In science, sometimes we would keep an extra significant figure so as not to loose information, even if we are not completely certain. We do that when we may use that result in further calculations. The drug content calculated for 10 individually analyzed tablets is one example.

Question 992257: Without using a calculator which is larger: x= 7^1/4 or y=4^1/3

Answer by Edwin McCravy(13211)   (Show Source):
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Which is larger? (without using a calculator)

Rewrite the exponents with a common denominator

Get them with a common fraction exponent:

Evaluate the bases without a calculator:

,

And since 343 > 256

So

Edwin

Question 992160: what is 15 to the 7 th power divided by 15 to the 4 th power?

Question 992051: (6n^4)^3 Do I do 6times 6 times 6times216 n^12
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The exponent is applied to each associated factor.

You could drag this to a lower level.

Question 992047: Which pair of numbers is closer together? 10^10 and 10^50 , or the pair 10^100 and 10^101?
I know 10^100 and 10^101 are much much further apart due to the exponent operating on a much larger scale, but I don't know how to prove this is mathematical notation. My calculator gives maths error for 10^101-10^100, so ideally I would like some algebraic way of proving the solution that doesn't simply rely on typing the numbers in.
Thanks.

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Which pair of numbers is closer together? 10^10 and 10^50 , or the pair 10^100 and 10^101?
I know 10^100 and 10^101 are much much further apart due to the exponent operating on a much larger scale, but I don't know how to prove this is mathematical notation. My calculator gives maths error for 10^101-10^100, so ideally I would like some algebraic way of proving the solution that doesn't simply rely on typing the numbers in.
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10^50-10^10 = 10^10[10^40-1]
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10^101-10^100 = 10^100[10-1] = 10^10[10^90]*9
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Since 10^90*9 > 10^40-1, 10^101-10^100 is a greater difference.
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Cheers,
Stan H.
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Question 991651: (8.9 × 10^-5)(3.2 × 10^-6)=
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Use associative property for multiplication and commutative property for multiplication, and rules of exponents.

Finish it.

Question 991683: Is the answer to (3 to the fifth power) then to the sixth power (243) the same as 3 to the fifth power then to the sixth power without any parentheses the same answer?

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.

.

.
No, they are not the same.

Question 991639: 8g to the fourth power divided by 6g to the 6th power
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8g^4 / 6g^6 = (8/6) * (g^4/g^6)

8/6 = 4/3

g^4/g^6 = g^(4-6) = g^(-2) = 1/g^2

you wind up with:

4/3 * 1/g^2 which can then be simplified to:

4 / 3g^2

Question 991370: Your classmate simplified the expression 6w to the 12th power divided by 3w to the 11th power = 2w to the 0 power = 2 times 0 = 0
Explain their error and write correct expression.

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The subtraction was wrong.
Also, .

Question 991569: (y/5)2nd power times (y/5)5th power divided by (y to the second power/5)6
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Instead of writing , I'll use for all the intermediate steps.

Question 991467: X/ (2x^0)^2
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X/ (2x^0)^2
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= X/(2*1)^2
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= X/(2)^2
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= X/4
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Cheers,
Stan H.
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Question 991341: 6 to the second power divided by 2(3)+4=

Question 991048: If 244n=1022base four find the value of n.

Question 991066: Rewrite the following without an exponent.
8^-2

Question 990664: Whats 450×89÷3x=x
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It's an equation.

Question 990650: G divided by g to the power of 2
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Question 990468: the base of a cylinder is a right triangle topped by a 60 degrees sector of a circle, as shown. if the dimensions are in meters and the height of the cylinder is 8 meters, what is the volume of the cylinder?
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What you have written makes absolutely no sense. The base of a cylinder is a right triangle? Absurd...

John

My calculator said it, I believe it, that settles it

Question 990607: 3 to the second power + (-4) to the second power
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3^2+(-4)^2=
9+16=25

Question 990458: how would i solve this equation?
9x the second power. divided by a-

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It is not an equation, therefore you cannot "solve" it.

John

My calculator said it, I believe it, that settles it

Question 990275: How to solve which are equivalent to a fraction with exponents?
EXAMPLE: 3 exponent 4
_____________
5 exponent 2

Question 990274: Which values are equivalent to the fraction below?
3 exponent 6
_____________
3 exponent 8
A. [1/3] exponent 48
B. 3 exponent 14
C. [1/3] exponent 2
D. 3 exponent -2
E. 1/9
F. 3 exponent 2

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3^6 / 3^8 = 1 / 3^2 = 3^(-2) = 1 / 9
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Question 990126: iam having a bit of a hard time with this problem help with be greatly thankful
(675 □ 9) x (4-3)=75