Select the equivalent expression. root(10)((s^(-1))/(s^(-6))) s^(-(1)/(2)) s^(-2) s^((1)/(2)) s^(2)

Understand the expression: Understand the given expression. We are given the expression root(10)((s^(-1))/(s^(-6))) and we need to simplify it to find the equivalent expression.Simplify inside the root: Simplify the expression inside the root. The expression inside the root is (s^(-1))/(s^(-6)). When dividing exponential expressions with the same base, we subtract the exponents. So, (s^(-1))/(s^(-6)) = s^(-1 - (-6)) = s^(6 - 1) = s^5.Apply the root: Apply the root to the simplified expression. Now we have root(10)(s^5). The 10th root of s^5 can be written as (s^5)^(1/10).Use power of a power rule: Use the power of a power rule. Using the power of a power rule, we multiply the exponents: (s^5)^(1/10) = s^(5*(1/10)) = s^(1/2).Identify equivalent expression: Identify the equivalent expression. The equivalent expression is s^(1/2), which is one of the options given.

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Select the equivalent expression.

root(10)((s^(-1))/(s^(-6)))

s^(-(1)/(2))

s^(-2)

s^((1)/(2))

s^(2)

Select the equivalent expression. $\newline$ $\sqrt[10]{\frac{s^{-1}}{s^{-6}}}$ $\newline$ $s^{-\frac{1}{2}}$ $\newline$ $s^{-2}$ $\newline$ $s^{\frac{1}{2}}$ $\newline$ $s^{2}$

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Math Problems

Algebra 1

Multiplication with rational exponents

Full solution

Q. Select the equivalent expression.

\newline

\sqrt[10]{\frac{s^{-1}}{s^{-6}}}

\newline

s^{-\frac{1}{2}}

\newline

s^{-2}

\newline

s^{\frac{1}{2}}

\newline

s^{2}

Understand the expression: Understand the given expression. $\newline$ We are given the expression $\sqrt[10]{\left(\frac{s^{-1}}{s^{-6}}\right)}$ and we need to simplify it to find the equivalent expression.
Simplify inside the root: Simplify the expression inside the root. $\newline$ The expression inside the root is $\frac{s^{-1}}{s^{-6}}$ . When dividing exponential expressions with the same base, we subtract the exponents. $\newline$ So, $\frac{s^{-1}}{s^{-6}} = s^{-1 - (-6)} = s^{6 - 1} = s^5$ .
Apply the root: Apply the root to the simplified expression. $\newline$ Now we have $\sqrt[10]{s^5}$ . The $10^{\text{th}}$ root of $s^5$ can be written as $(s^5)^{\frac{1}{10}}$ .
Use power of a power rule: Use the power of a power rule. $\newline$ Using the power of a power rule, we multiply the exponents: $(s^5)^{\frac{1}{10}} = s^{5*\frac{1}{10}} = s^{\frac{1}{2}}$ .
Identify equivalent expression: Identify the equivalent expression. $\newline$ The equivalent expression is $s^{\frac{1}{2}}$ , which is one of the options given.