Select the equivalent expression. ((r^(-7))/(r^(4)))^((3)/(11)) (1)/(root(3)(r)) (1)/(r^(3)) root(3)(r) r^(3)

Simplify Exponents: Simplify the expression inside the parentheses by using the properties of exponents. When dividing like bases, subtract the exponents. (r^(-7))/(r^(4)) = r^(-7 - 4) = r^(-11)Apply Outer Exponent: Apply the outer exponent to the simplified base. Now we have (r^(-11))^((3)/(11)). When raising a power to a power, multiply the exponents. (r^(-11))^((3)/(11)) = r^(-11 * (3)/(11)) = r^(-3)Rewrite Negative Exponent: Rewrite the negative exponent as a reciprocal. A negative exponent indicates the reciprocal of the base raised to the positive of that exponent. r^(-3) = 1/(r^(3))Compare with Options: Compare the result with the given options. The expression 1/(r^(3)) matches one of the given options.

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Select the equivalent expression.

((r^(-7))/(r^(4)))^((3)/(11))

(1)/(root(3)(r))

(1)/(r^(3))

root(3)(r)

r^(3)

Select the equivalent expression. $\newline$ $\left(\frac{r^{-7}}{r^{4}}\right)^{\frac{3}{11}}$ $\newline$ $\frac{1}{\sqrt[3]{r}}$ $\newline$ $\frac{1}{r^{3}}$ $\newline$ $\sqrt[3]{r}$ $\newline$ $r^{3}$

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Math Problems

Algebra 1

Multiplication with rational exponents

Full solution

Q. Select the equivalent expression.

\newline

\left(\frac{r^{-7}}{r^{4}}\right)^{\frac{3}{11}}

\newline

\frac{1}{\sqrt[3]{r}}

\newline

\frac{1}{r^{3}}

\newline

\sqrt[3]{r}

\newline

r^{3}

Simplify Exponents: Simplify the expression inside the parentheses by using the properties of exponents. $\newline$ When dividing like bases, subtract the exponents. $\newline$ $(r^{(-7)})/(r^{(4)}) = r^{(-7 - 4)} = r^{(-11)}$
Apply Outer Exponent: Apply the outer exponent to the simplified base. $\newline$ Now we have $(r^{-11})^{(3)/(11)}$ . $\newline$ When raising a power to a power, multiply the exponents. $\newline$ $(r^{-11})^{(3)/(11)} = r^{-11 \times (3)/(11)} = r^{-3}$
Rewrite Negative Exponent: Rewrite the negative exponent as a reciprocal. $\newline$ A negative exponent indicates the reciprocal of the base raised to the positive of that exponent. $\newline$ $r^{-3} = \frac{1}{r^{3}}$
Compare with Options: Compare the result with the given options. $\newline$ The expression $\frac{1}{r^{3}}$ matches one of the given options.