Rewriting expressions

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HiSET › Rewriting expressions

Questions 1 - 4

1

Rewrite as a single power of :

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

$y^{9}$

$y^{8}$

$y^{7}$

$y^{12}$

$y^{18}$

Explanation

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.

2

Rewrite the expression $\sqrt{x} \cdot \sqrt[3]{x}$ as a single radical expression.

$\sqrt[6]{x^{5}}$

$\sqrt[6]{x }$

$\sqrt[5]{x }$

$\sqrt[5]{x^{6} }$

$\sqrt[3]{x^{2}}$

Explanation

First, rewrite each radical expression using rational exponents:

$\sqrt{x} = x ^{\frac{1}{2}}$

$\sqrt[3]{x} = x ^{\frac{1}{3}}$

Multiply these expressions using the Product of Powers Property:

$\sqrt{x} \cdot \sqrt[3]{x}$

$= x ^{\frac{1}{2}} \cdot x ^{\frac{1}{3}}$

$= x ^{\frac{1}{2}+\frac{1}{3}}$

$= x ^{\frac{3}{6}+\frac{2}{6}}$

$= x ^{\frac{5}{6}}$

This can be rewritten in radical form as $\sqrt[6]{x^{5}}$ .

3

Rewrite the expression $\sqrt{x} \cdot \sqrt[3]{x}$ as a single radical expression.

$\sqrt[6]{x^{5}}$

$\sqrt[6]{x }$

$\sqrt[5]{x }$

$\sqrt[5]{x^{6} }$

$\sqrt[3]{x^{2}}$

Explanation

First, rewrite each radical expression using rational exponents:

$\sqrt{x} = x ^{\frac{1}{2}}$

$\sqrt[3]{x} = x ^{\frac{1}{3}}$

Multiply these expressions using the Product of Powers Property:

$\sqrt{x} \cdot \sqrt[3]{x}$

$= x ^{\frac{1}{2}} \cdot x ^{\frac{1}{3}}$

$= x ^{\frac{1}{2}+\frac{1}{3}}$

$= x ^{\frac{3}{6}+\frac{2}{6}}$

$= x ^{\frac{5}{6}}$

This can be rewritten in radical form as $\sqrt[6]{x^{5}}$ .

4

Rewrite as a single power of :

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

$y^{9}$

$y^{8}$

$y^{7}$

$y^{12}$

$y^{18}$

Explanation

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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