# Quotient of Powers

How to solve the quotient of powers a^{m}/a^{n}: formula, 2 examples, and their solutions.

## Formula

### Formula

a^{m}/a^{n} = a^{m - n}

(a ≠ 0)

When dividing the same base powers, subtract the exponents: m - n.

Product of Powers

## Example 1

### Example

### Solution

x^{8} and x^{3} have the same base: x.

So x^{8}/x^{3} = x^{8 - 3}.

8 - 3 = 5.

So x^{5} is the answer.

## Example 2

### Example

The bases are x, y, and z.

Use the formula to combine the same base powers.

### Solution

First simplify the coefficient numbers.

(= numbers in front of x, y, z)

12/4 = 3

So Write 3.

x^{7} and x^{4} have the same base: x.

So x^{7}/x^{4} = x^{7 - 4}.

The same y^{2} are in both of the numerator and the denominator.

So cancel both y^{2}.

So write 1.

z^{9} and z^{5} have the same base: z.

So z^{9}/z^{5} = z^{9 - 5}.

So the given expresssion is 3⋅x^{7 - 4}⋅1⋅z^{9 - 5}.

The same base powers are combined.

Simplify the exponents.

7 - 4 = 3

9 - 5 = 4

So 3x^{3}z^{4} is the answer.