Select the equivalent expression. (r^(7)*r^(-8))^((1)/(4)) r^(4) root(4)(r) (1)/(root(4)(r)) (1)/(r^(4))

Combine Exponents: Simplify the expression inside the parentheses by combining the exponents. When multiplying powers with the same base, you add the exponents. r^(7) * r^(-8) = r^(7 + (-8)) = r^(-1)Apply Outer Exponent: Apply the outer exponent to the simplified base. Now we have (r^(-1))^((1)/(4)). When raising a power to a power, you multiply the exponents. (r^(-1))^((1)/(4)) = r^(-1 * (1)/(4)) = r^(-1/4)Rewrite Negative Exponent: Rewrite the negative exponent as a reciprocal. A negative exponent means that the base is on the wrong side of the fraction line, so we take the reciprocal and make the exponent positive. r^(-1/4) = (1)/(r^(1/4))Recognize Fourth Root: Recognize that r^(1/4) is the fourth root of r. The expression (1)/(r^(1/4)) can be rewritten using the radical notation for roots. (1)/(r^(1/4)) = (1)/(root(4)(r))

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Select the equivalent expression.

(r^(7)*r^(-8))^((1)/(4))

r^(4)

root(4)(r)

(1)/(root(4)(r))

(1)/(r^(4))

Select the equivalent expression. $\newline$ $\left(r^{7} \cdot r^{-8}\right)^{\frac{1}{4}}$ $\newline$ $r^{4}$ $\newline$ $\sqrt[4]{r}$ $\newline$ $\frac{1}{\sqrt[4]{r}}$ $\newline$ $\frac{1}{r^{4}}$

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Math Problems

Algebra 1

Multiplication with rational exponents

Full solution

Q. Select the equivalent expression.

\newline

\left(r^{7} \cdot r^{-8}\right)^{\frac{1}{4}}

\newline

r^{4}

\newline

\sqrt[4]{r}

\newline

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

\newline

\frac{1}{r^{4}}

Combine Exponents: Simplify the expression inside the parentheses by combining the exponents. $\newline$ When multiplying powers with the same base, you add the exponents. $\newline$ $r^{7} \times r^{-8} = r^{7 + (-8)} = r^{-1}$
Apply Outer Exponent: Apply the outer exponent to the simplified base. $\newline$ Now we have $(r^{-1})^{\left(\frac{1}{4}\right)}$ . When raising a power to a power, you multiply the exponents. $\newline$ $(r^{-1})^{\left(\frac{1}{4}\right)} = r^{-1 \times \left(\frac{1}{4}\right)} = r^{-\frac{1}{4}}$
Rewrite Negative Exponent: Rewrite the negative exponent as a reciprocal. $\newline$ A negative exponent means that the base is on the wrong side of the fraction line, so we take the reciprocal and make the exponent positive. $\newline$ $r^{-\frac{1}{4}} = \frac{1}{r^{\frac{1}{4}}}$
Recognize Fourth Root: Recognize that $r^{1/4}$ is the fourth root of $r$ . The expression $(1)/(r^{1/4})$ can be rewritten using the radical notation for roots. $(1)/(r^{1/4}) = (1)/\sqrt[4]{r}$