Product of Powers

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

Formula

Formula

am⋅an = am + n
When multiplying the same base powers, add the exponents (m + n).

Example 1

Example

Solution

x6 and x8 have the same base: x.
So x6⋅x8 = x6 + 8.

6 + 8 = 14.

So x14 is the answer.

Example 2

Example

The bases of the powers are 3, x, and y.
Use the formula to combine the same base powers.

Solution

32 and 3 have the same base: 3.
So 32⋅3 = 32 + 1.

x and x3 have the same base: x.
So x⋅x3 = x1 + 3.

y4 and y7 have the same base: y.
So y4⋅y7 = y4 + 7.

So the given expresssion is 32 + 1⋅x1 + 3⋅y4 + 7.
The same base powers are combined.

Simplify the exponents.
2 + 1 = 3
1 + 3 = 4
4 + 7 = 11

33 = 27

So 27x4y11 is the answer.