Power of a Product

If the base is a product, we can distribute the exponent to the terms of the base.

For example, (4 ⋅ 5)³ is equal to

(4 ⋅ 5) ⋅ (4 ⋅ 5) ⋅ (4 ⋅ 5)

We can rearrange this expression to:

(4 ⋅ 4 ⋅ 4) ⋅ (5 ⋅ 5 ⋅ 5)

This is equal to:

4³ ⋅ 5³

Thus we can conclude that:

(4 ⋅ 5)³ = 4³ ⋅ 5³

In general:

(x ⋅ y)ⁿ = (xⁿ) ⋅ (yⁿ)

Here are some examples:

(2 ⋅ 3)⁴ = (2⁴) ⋅ (3⁴)

((x + 1) ⋅ 5)⁷ = ((x + 1)⁷) ⋅ (5⁷)

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