# Power of a Quotient

How to solve the product of powers (a^{m}⋅a^{n}): formula, 2 examples, and their solutions.

## Formula

### Formula

(a/b)^{m} = a^{m}/b^{m}

(a ≠ 0)

Just like (ab)^{m} formula, power the numbers in the parentheses: a^{m}, b^{m}.

## Example 1

### Example

### Solution

Cube x and y^{2}.

So (x/y^{2})^{3} = x^{3}/(y^{2})^{3}.

(y^{2})^{3} = y^{2⋅3} = y^{6}

Power of a Power

So x^{3}/y^{6} 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, x^{4}, and y.

Then write 3^{2} (x^{4})^{2} over y^{2}.

Next, cube y, 2, and x.

Then write y^{3} over 2^{3} x^{3}.

So the given expresssion is

[(3^{2} (x^{4})^{2})/y^{2}] [y^{3}/(2^{3} x^{3})].

3^{2} = 9

(x^{4})^{2} = x^{4⋅2} = x^{8}

Power of a Power

2^{3} = 8

x^{8}/x^{3} = x^{8 - 3} = x^{5}

y^{3}/y^{2} = y^{3 - 2} = y

Quotient of Powers

3^{3} = 27

So 9x^{5}y/8 is the answer.