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HiSET: Math : Rational exponents and the properties of exponents

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Example Questions

Example Question #31 : Numbers And Operations On Numbers

Rewrite as a single power of $\displaystyle y$ :

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

Possible Answers:

$y^{7}$ $\displaystyle y^{7}$

$y^{9}$ $\displaystyle y^{9}$

$y^{8}$ $\displaystyle y^{8}$

$y^{12}$ $\displaystyle y^{12}$

$y^{18}$ $\displaystyle y^{18}$

Correct answer:

$y^{9}$ $\displaystyle y^{9}$

Explanation:

Apply the properties of exponents to the expression as follows:

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

By the Power of a Power Property:

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

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

Restating:

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

By the Product of Powers of Property:

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

$= y^{9}$ $\displaystyle = y^{9}$ ,

the correct response.

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HiSET: Math : Rational exponents and the properties of exponents

Study concepts, example questions & explanations for HiSET: Math

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Example Question #31 : Numbers And Operations On Numbers

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