Select the equivalent expression. root(15)(s^(-7)*s^(2)) s^((1)/(3)) s^(-(1)/(3)) s^(-3) s^(3)

Simplify Exponent Expression: Simplify the expression inside the root. We have the expression root(15)(s^(-7)*s^(2)). To simplify the expression inside the root, we use the property of exponents that states when multiplying like bases, we add the exponents. s^(-7) * s^(2) = s^(-7 + 2) = s^(-5)Apply Root: Apply the root to the simplified expression. Now we have root(15)(s^(-5)). The 15th root of s^(-5) can be written as s^(-5/15), which simplifies to s^(-1/3).Match to Options: Match the simplified expression to the given options. The expression s^(-1/3) matches one of the given options, which is s^(-(1)/(3)).

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Select the equivalent expression.

root(15)(s^(-7)*s^(2))

s^((1)/(3))

s^(-(1)/(3))

s^(-3)

s^(3)

Select the equivalent expression. $\newline$ $\sqrt[15]{s^{-7} \cdot s^{2}}$ $\newline$ $s^{\frac{1}{3}}$ $\newline$ $s^{-\frac{1}{3}}$ $\newline$ $s^{-3}$ $\newline$ $s^{3}$

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Math Problems

Algebra 1

Multiplication with rational exponents

Full solution

Q. Select the equivalent expression.

\newline

\sqrt[15]{s^{-7} \cdot s^{2}}

\newline

s^{\frac{1}{3}}

\newline

s^{-\frac{1}{3}}

\newline

s^{-3}

\newline

s^{3}

Simplify Exponent Expression: Simplify the expression inside the root. $\newline$ We have the expression $\sqrt[15]{s^{-7}\cdot s^{2}}$ . To simplify the expression inside the root, we use the property of exponents that states when multiplying like bases, we add the exponents. $\newline$ $s^{-7} \cdot s^{2} = s^{-7 + 2} = s^{-5}$
Apply Root: Apply the root to the simplified expression. $\newline$ Now we have $\sqrt[15]{s^{-5}}$ . The $15^{\text{th}}$ root of $s^{-5}$ can be written as $s^{-5/15}$ , which simplifies to $s^{-1/3}$ .
Match to Options: Match the simplified expression to the given options. $\newline$ The expression $s^{(-1/3)}$ matches one of the given options, which is $s^{-(1)/(3)}$ .