Power of a Quotient

How to solve the product of powers (am⋅an): formula, 2 examples, and their solutions.

Formula

Formula

(a/b)m = am/bm
(a ≠ 0)
Just like (ab)m formula, power the numbers in the parentheses: am, bm.

Example 1

Example

Solution

Cube x and y2.
So (x/y2)3 = x3/(y2)3.

(y2)3 = y2⋅3 = y6

Power of a Power

So x3/y6 is the answer.

Example 2

Example

Both (a/b)m formula and (ab)m formula powers the numbers in the parentheses.
So you can directly use these two formulas together.

Solution

First square 3, x4, and y.
Then write 32 (x4)2 over y2.

Next, cube y, 2, and x.
Then write y3 over 23 x3.

So the given expresssion is
[(32 (x4)2)/y2] [y3/(23 x3)].

32 = 9
(x4)2 = x4⋅2 = x8

Power of a Power

23 = 8

x8/x3 = x8 - 3 = x5
y3/y2 = y3 - 2 = y

Quotient of Powers

33 = 27

So 9x5y/8 is the answer.