Quotient of Powers

How to solve the quotient of powers am/an: formula, 2 examples, and their solutions.

Formula

Formula

am/an = am - n
(a ≠ 0)
When dividing the same base powers, subtract the exponents: m - n.

Product of Powers

Example 1

Example

Solution

x8 and x3 have the same base: x.
So x8/x3 = x8 - 3.

8 - 3 = 5.

So x5 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.

x7 and x4 have the same base: x.
So x7/x4 = x7 - 4.

The same y2 are in both of the numerator and the denominator.
So cancel both y2.
So write 1.

z9 and z5 have the same base: z.
So z9/z5 = z9 - 5.

So the given expresssion is 3⋅x7 - 4⋅1⋅z9 - 5.
The same base powers are combined.

Simplify the exponents.
7 - 4 = 3
9 - 5 = 4

So 3x3z4 is the answer.