How to Multiply Powers in Parentheses

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This entry is a continuation of Rules 1 and 2 about powers, and Rules 3 and 4 about dividing powers.

Rules 5 and 6, presented here, are about powers of parentheses. When you have learned these rules, you should practice examples combining the rules.

Rule 5

Rule

Parentheses and Powers—Multiplication

(a b)n = an bn

Let’s use an example to see why:

a3 = a a a and b3 = b b b

That leads to

(ab)3 = ab ab ab = a b a b a b = a a a b b b = a3 b3.

Example 1

Write (2x)3 as simply as possible

(2x)3 = 23x3 = 8x3

Write (2a)4 as simply as possible

(2a)4 = 24a4 = 16a4

Rule 6

Rule

Parentheses and Powers—Division

(a b)n = an bn

Let’s use an example to see why:

a3 = a a a and b3 = b b b

Therefore

(a b )3 = a b a b a b = a a a b b b = a3 b3

Example 2

Write (3 x) 3 as simply as possible

(3 x) 3 = 33 x3 = 27 x3

Write (x y) 2 as simply as possible

(x y )2 = x2 y2

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