Question

Simplify the expression. Write your answer as a power.

(xy)⁷
The simplified expression is

Answer 1

x⁷y⁷

Explanation:

An exponent signifies the base is a repeated factor in the product. The exponent is the number of times it is a factor.

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The term (xy)^7 means (xy) is a factor 7 times:

= (xy)·(xy)·(xy)·(xy)·(xy)·(xy)·(xy)

The commutative and associative properties of multiplication let us rearrange this to ...

= (x·x·x·x·x·x·x)·(y·y·y·y·y·y·y)

= (x^7)(y^7)

The expression can be simplified to ...

`(xy)^7 =\boxed{x^7y^7}`

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The rule of exponents is ...

(ab)^c = (a^c)(b^c)