Select the equivalent expression. ((s^(-8))/(s^(7)))^((1)/(6)) (1)/(sqrt(s^(5))) root(5)(s^(2)) (1)/(root(5)(s^(2))) sqrt(s^(5))

Simplify Exponents: Simplify the expression inside the parentheses by using the laws of exponents. When dividing powers with the same base, subtract the exponents. (s^(-8))/(s^(7)) = s^(-8 - 7) = s^(-15)Apply Exponent Rule: Apply the exponent outside the parentheses to the simplified base. (s^(-15))^((1)/(6)) = s^(-15 * (1/6)) = s^(-15/6) = s^(-5/2)Convert to Positive Exponent: Convert the negative exponent to a positive exponent by taking the reciprocal of the base. s^(-5/2) = 1/(s^(5/2))Rewrite with Radical: Rewrite the expression with a radical to represent the fractional exponent. 1/(s^(5/2)) = 1/(sqrt(s^(5)))Compare with Options: Compare the result with the given options. The equivalent expression is 1/(sqrt(s^(5))).

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Select the equivalent expression.

((s^(-8))/(s^(7)))^((1)/(6))

(1)/(sqrt(s^(5)))

root(5)(s^(2))

(1)/(root(5)(s^(2)))

sqrt(s^(5))

Select the equivalent expression. $\newline$ $\left(\frac{s^{-8}}{s^{7}}\right)^{\frac{1}{6}}$ $\newline$ $\frac{1}{\sqrt{s^{5}}}$ $\newline$ $\sqrt[5]{s^{2}}$ $\newline$ $\frac{1}{\sqrt[5]{s^{2}}}$ $\newline$ $\sqrt{s^{5}}$

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Math Problems

Algebra 1

Multiplication with rational exponents

Full solution

Q. Select the equivalent expression.

\newline

\left(\frac{s^{-8}}{s^{7}}\right)^{\frac{1}{6}}

\newline

\frac{1}{\sqrt{s^{5}}}

\newline

\sqrt[5]{s^{2}}

\newline

\frac{1}{\sqrt[5]{s^{2}}}

\newline

\sqrt{s^{5}}

Simplify Exponents: Simplify the expression inside the parentheses by using the laws of exponents. $\newline$ When dividing powers with the same base, subtract the exponents. $\newline$ $(s^{(-8)})/(s^{(7)}) = s^{(-8 - 7)} = s^{(-15)}$
Apply Exponent Rule: Apply the exponent outside the parentheses to the simplified base. $\newline$ $(s^{-15})^{\frac{1}{6}} = s^{-15 \times \frac{1}{6}} = s^{-\frac{15}{6}} = s^{-\frac{5}{2}}$
Convert to Positive Exponent: Convert the negative exponent to a positive exponent by taking the reciprocal of the base. $\newline$ $s^{(-\frac{5}{2})} = \frac{1}{s^{(\frac{5}{2})}}$
Rewrite with Radical: Rewrite the expression with a radical to represent the fractional exponent. $\newline$ $\frac{1}{s^{\frac{5}{2}}} = \frac{1}{\sqrt{s^{5}}}$
Compare with Options: Compare the result with the given options. The equivalent expression is $\frac{1}{\sqrt{s^{5}}}$ .