# Power of a Quotient

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

## Formula

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

(a ≠ 0)

Just like (ab)^{m} formula,

power the numbers in the parentheses.

## Example(x/y^{2})^{3}

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([3x^{4}/y])^{2}⋅(y/[2x])^{3}

Both (a/b)^{m} formula and (ab)^{m} formula

powers the numbers in the parentheses.

So directly use these two formulas together.

First square 3, x^{4}, and y.

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

Next, cube y, 2, and x.

Then write [y^{3}]/[2^{3}⋅x^{3}].

So (given) = [(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

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