Select the equivalent expression. ((b^(8))/(b^(4)))^((1)/(2)) (1)/(b^(2)) b^(2) (1)/(sqrtb) sqrtb

Simplify Exponents: Simplify the expression inside the parentheses using the properties of exponents. When dividing like bases with exponents, subtract the exponents. (b^(8))/(b^(4)) = b^(8-4) = b^(4)Apply Exponent Rule: Apply the exponent outside the parentheses to the result from Step 1. (b^(4))^((1)/(2)) means taking the square root of b^(4). The square root of b^(4) is b^(4*(1/2)) = b^(2).Check Final Result: Check the final result against the given options. The equivalent expression is b^(2).

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Select the equivalent expression.

((b^(8))/(b^(4)))^((1)/(2))

(1)/(b^(2))

b^(2)

(1)/(sqrtb)

sqrtb

Select the equivalent expression. $\newline$ $\left(\frac{b^{8}}{b^{4}}\right)^{\frac{1}{2}}$ $\newline$ $\frac{1}{b^{2}}$ $\newline$ $b^{2}$ $\newline$ $\frac{1}{\sqrt{b}}$ $\newline$ $\sqrt{b}$

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Math Problems

Algebra 1

Multiplication with rational exponents

Full solution

Q. Select the equivalent expression.

\newline

\left(\frac{b^{8}}{b^{4}}\right)^{\frac{1}{2}}

\newline

\frac{1}{b^{2}}

\newline

b^{2}

\newline

\frac{1}{\sqrt{b}}

\newline

\sqrt{b}

Simplify Exponents: Simplify the expression inside the parentheses using the properties of exponents. $\newline$ When dividing like bases with exponents, subtract the exponents. $\newline$ $\frac{b^{8}}{b^{4}} = b^{8-4} = b^{4}$
Apply Exponent Rule: Apply the exponent outside the parentheses to the result from Step $1$ . $\newline$ $(b^{4})^{(\frac{1}{2})}$ means taking the square root of $b^{4}$ . $\newline$ The square root of $b^{4}$ is $b^{4*(\frac{1}{2})} = b^{2}$ .
Check Final Result: Check the final result against the given options. $\newline$ The equivalent expression is $b^{2}$ .