Select the equivalent expression. (x^(-8)*x^(-5))^((4)/(13)) x^(4) (1)/(x^(4)) (1)/(root(4)(x)) root(4)(x)

Apply Exponent Rule: Apply the exponent rule for multiplying powers with the same base. When multiplying powers with the same base, we add the exponents. x^(-8) * x^(-5) = x^(-8 + -5) = x^(-13)Apply Power of Power Rule: Apply the power of a power rule. When raising a power to another power, we multiply the exponents. (x^(-13))^((4)/(13)) = x^(-13 * (4)/(13)) = x^(-52/13) = x^(-4)Rewrite with Positive Exponent: Rewrite the expression with a positive exponent. x^(-4) is equivalent to 1/(x^(4)).

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Select the equivalent expression.

(x^(-8)*x^(-5))^((4)/(13))

x^(4)

(1)/(x^(4))

(1)/(root(4)(x))

root(4)(x)

Select the equivalent expression. $\newline$ $\left(x^{-8} \cdot x^{-5}\right)^{\frac{4}{13}}$ $\newline$ $x^{4}$ $\newline$ $\frac{1}{x^{4}}$ $\newline$ $\frac{1}{\sqrt[4]{x}}$ $\newline$ $\sqrt[4]{x}$

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Math Problems

Algebra 1

Multiplication with rational exponents

Full solution

Q. Select the equivalent expression.

\newline

\left(x^{-8} \cdot x^{-5}\right)^{\frac{4}{13}}

\newline

x^{4}

\newline

\frac{1}{x^{4}}

\newline

\frac{1}{\sqrt[4]{x}}

\newline

\sqrt[4]{x}

Apply Exponent Rule: Apply the exponent rule for multiplying powers with the same base. $\newline$ When multiplying powers with the same base, we add the exponents. $\newline$ $x^{-8} \times x^{-5} = x^{-8 + -5}$ $\newline$ $= x^{-13}$
Apply Power of Power Rule: Apply the power of a power rule. $\newline$ When raising a power to another power, we multiply the exponents. $\newline$ $(x^{(-13)})^{(\frac{4}{13})} = x^{(-13 \cdot (\frac{4}{13}))}$ $\newline$ $= x^{(-\frac{52}{13})}$ $\newline$ $= x^{(-4)}$
Rewrite with Positive Exponent: Rewrite the expression with a positive exponent. $x^{-4}$ is equivalent to $1/(x^{4})$ .