Rational exponents and the properties of exponents - HiSet: High School Equivalency Test: Math

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Question

Rewrite as a single power of :

$(y^{2})^{3} \cdot y (y^{2})$

Answer

Apply the properties of exponents to the expression as follows:

$(y^{2})^{3} \cdot y (y^{2})$

By the Power of a Power Property:

$= (y^{2 \cdot 3})\cdot y (y^{2})$

$= (y^{6})\cdot y (y^{2})$

Restating:

$= y^{6} \cdot y^{1} \cdot y^{2}$

By the Product of Powers of Property:

$= y^{6+1+2}$

$= y^{9}$ ,

the correct response.

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