Select the equivalent expression. root(4)((y^(-7))/(y^(-5))) y^((1)/(2)) y^(2) y^(-(1)/(2)) y^(-2)

Simplify Expression: Simplify the expression inside the radical. We have the expression root(4)((y^(-7))/(y^(-5))). To simplify the expression inside the radical, we use the property of exponents that states when dividing like bases, we subtract the exponents. So, (y^(-7))/(y^(-5)) = y^(-7 - (-5)) = y^(-7 + 5) = y^(-2).Apply Fourth Root: Apply the fourth root to the simplified expression. Now we apply the fourth root to y^(-2). The fourth root of a variable to an exponent is the same as raising the variable to the exponent divided by 4. So, root(4)(y^(-2)) = y^(-2/4) = y^(-1/2).Match Answer Choices: Match the simplified expression to the answer choices. The simplified expression is y^(-1/2). Looking at the answer choices, we see that y^(-1/2) matches the third option: y^(-(1)/(2)).

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Select the equivalent expression.

root(4)((y^(-7))/(y^(-5)))

y^((1)/(2))

y^(2)

y^(-(1)/(2))

y^(-2)

Select the equivalent expression. $\newline$ $\sqrt[4]{\frac{y^{-7}}{y^{-5}}}$ $\newline$ $y^{\frac{1}{2}}$ $\newline$ $y^{2}$ $\newline$ $y^{-\frac{1}{2}}$ $\newline$ $y^{-2}$

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Math Problems

Algebra 1

Multiplication with rational exponents

Full solution

Q. Select the equivalent expression.

\newline

\sqrt[4]{\frac{y^{-7}}{y^{-5}}}

\newline

y^{\frac{1}{2}}

\newline

y^{2}

\newline

y^{-\frac{1}{2}}

\newline

y^{-2}

Simplify Expression: Simplify the expression inside the radical. $\newline$ We have the expression $\sqrt[4]{\frac{y^{-7}}{y^{-5}}}$ . To simplify the expression inside the radical, we use the property of exponents that states when dividing like bases, we subtract the exponents. $\newline$ So, $\frac{y^{-7}}{y^{-5}} = y^{-7 - (-5)} = y^{-7 + 5} = y^{-2}$ .
Apply Fourth Root: Apply the fourth root to the simplified expression. $\newline$ Now we apply the fourth root to $y^{-2}$ . The fourth root of a variable to an exponent is the same as raising the variable to the exponent divided by $4$ . $\newline$ So, $\sqrt[4]{y^{-2}} = y^{-\frac{2}{4}} = y^{-\frac{1}{2}}$ .
Match Answer Choices: Match the simplified expression to the answer choices. $\newline$ The simplified expression is $y^{-\frac{1}{2}}$ . Looking at the answer choices, we see that $y^{-\frac{1}{2}}$ matches the third option: $y^{-\left(\frac{1}{2}\right)}$ .