Power of a Product

Consider the following:

(4⋅5)3

= (4⋅5)⋅(4⋅5)⋅(4⋅5)

We can rearrange the operation above to:

= (4⋅4⋅4)⋅(5⋅5⋅5)

We can rewrite the above as:

= 43⋅53

Thus we can conclude:

(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)

Quiz (1 point)

Consider the following:

(11 ⋅ 12)2) = 112 ⋅ x2

What is x?

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