Question

Please Help!!!
(3/2b^4)^3

Answer 1

Is this the question?

\(\LARGE \left( \dfrac{3}{2b^4} \right)^3\)

Answer 2

When you raise a fraction to a power, you raise the numerator and the denominator to that power.

Answer 3

yes

Answer 4

First, raise the numerator and the denominator to the 3rd power:

\(\LARGE \left( \dfrac{3}{2b^4} \right)^3 = \dfrac{3^3}{(2b^4)^3}\)

Answer 5

The numerator is simple, \(3^3\) is simply \(27\).

Answer 6

Now we need to work on the denominator.

Answer 7

When you raise a product to a power, you raise each factor of the product to that power.

Answer 8

\( \LARGE =\dfrac{27}{2^3(b^4)^3}\)

Answer 9

\(2^3\) is smple. It is \(8\).

Answer 10

Now we need to deal with \((b^4)^3\).

Answer 11

When you raise a power to a power, you multiply powers.

Answer 12

\( \LARGE =\dfrac{27}{8b^{12}}\)

Answer 13

that would be b12?

Answer 14

Thank you soooo much!!!!!!! I needed that help thank you

Answer 15

b to the 12th power.

Answer 16

Here are the three rules of exponents we used:

\(\left(\dfrac{a}{b}\right)^n = \dfrac{a^n}{b^n}\)

\((ab)^n = a^nb^n\)

\((a^m)^n = a ^{mn} \)

Answer 17

You are welcome.