Select the equivalent expression. root(8)((b^(-8))/(b^(-6))) b^(-4) b^(-(1)/(4)) b^((1)/(4)) b^(4)

Simplify Exponent Division: Simplify the expression inside the radical. We have the expression root(8)((b^(-8))/(b^(-6))). To simplify the expression inside the radical, we use the property of exponents that states when dividing like bases, we subtract the exponents. So, (b^(-8))/(b^(-6)) = b^(-8 - (-6)) = b^(-8 + 6) = b^(-2).Apply Radical: Apply the radical to the simplified expression. Now we have root(8)(b^(-2)). The 8th root of b^(-2) can be written as (b^(-2))^(1/8). Using the property of exponents (a^(m))^n = a^(m*n), we get b^(-2 * 1/8) = b^(-1/4).Check Answer Choices: Check the answer choices for the equivalent expression. We have simplified the expression to b^(-1/4). Now we compare this with the given answer choices. The correct answer choice that matches b^(-1/4) is b^(-(1)/(4)).

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Select the equivalent expression.

root(8)((b^(-8))/(b^(-6)))

b^(-4)

b^(-(1)/(4))

b^((1)/(4))

b^(4)

Select the equivalent expression. $\newline$ $\sqrt[8]{\frac{b^{-8}}{b^{-6}}}$ $\newline$ $b^{-4}$ $\newline$ $b^{-\frac{1}{4}}$ $\newline$ $b^{\frac{1}{4}}$ $\newline$ $b^{4}$

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Math Problems

Algebra 1

Multiplication with rational exponents

Full solution

Q. Select the equivalent expression.

\newline

\sqrt[8]{\frac{b^{-8}}{b^{-6}}}

\newline

b^{-4}

\newline

b^{-\frac{1}{4}}

\newline

b^{\frac{1}{4}}

\newline

b^{4}

Simplify Exponent Division: Simplify the expression inside the radical. $\newline$ We have the expression $\sqrt[8]{\frac{b^{-8}}{b^{-6}}}$ . 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, $\frac{b^{-8}}{b^{-6}} = b^{-8 - (-6)} = b^{-8 + 6} = b^{-2}$ .
Apply Radical: Apply the radical to the simplified expression. $\newline$ Now we have $\sqrt[8]{b^{-2}}$ . The $8$ th root of $b^{-2}$ can be written as $(b^{-2})^{\frac{1}{8}}$ . $\newline$ Using the property of exponents $(a^{m})^{n} = a^{m*n}$ , we get $b^{-2 * \frac{1}{8}} = b^{-\frac{1}{4}}$ .
Check Answer Choices: Check the answer choices for the equivalent expression. $\newline$ We have simplified the expression to $b^{-\frac{1}{4}}$ . Now we compare this with the given answer choices. $\newline$ The correct answer choice that matches $b^{-\frac{1}{4}}$ is $b^{-\left(\frac{1}{4}\right)}$ .