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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