Select the equivalent expression. (n^(-2)*n^(-8))^((3)/(10)) n^(3) root(3)(n) (1)/(root(3)(n)) (1)/(n^(3))

Simplify base with exponents: Simplify the base by adding the exponents. When multiplying two powers with the same base, you add the exponents. n^(-2) * n^(-8) = n^(-2 + -8) = n^(-10)Apply outer exponent: Apply the outer exponent to the simplified base. Now we have (n^(-10))^((3)/(10)). When raising a power to a power, you multiply the exponents. (n^(-10))^((3)/(10)) = n^(-10 * (3)/(10)) = n^(-3)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 you flip it to make the exponent positive. n^(-3) = 1/(n^(3))

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Select the equivalent expression.

(n^(-2)*n^(-8))^((3)/(10))

n^(3)

root(3)(n)

(1)/(root(3)(n))

(1)/(n^(3))

Select the equivalent expression. $\newline$ $\left(n^{-2} \cdot n^{-8}\right)^{\frac{3}{10}}$ $\newline$ $n^{3}$ $\newline$ $\sqrt[3]{n}$ $\newline$ $\frac{1}{\sqrt[3]{n}}$ $\newline$ $\frac{1}{n^{3}}$

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Math Problems

Algebra 1

Multiplication with rational exponents

Full solution

Q. Select the equivalent expression.

\newline

\left(n^{-2} \cdot n^{-8}\right)^{\frac{3}{10}}

\newline

n^{3}

\newline

\sqrt[3]{n}

\newline

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

\newline

\frac{1}{n^{3}}

Simplify base with exponents: Simplify the base by adding the exponents. $\newline$ When multiplying two powers with the same base, you add the exponents. $\newline$ $n^{-2} \times n^{-8} = n^{-2 + -8}$ $\newline$ $= n^{-10}$
Apply outer exponent: Apply the outer exponent to the simplified base. $\newline$ Now we have $(n^{(-10)})^{(\frac{3}{10})}$ . When raising a power to a power, you multiply the exponents. $\newline$ $(n^{(-10)})^{(\frac{3}{10})} = n^{(-10 \cdot (\frac{3}{10}))}$ $\newline$ = $n^{(-3)}$
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 you flip it to make the exponent positive. $\newline$ $n^{-3} = \frac{1}{n^{3}}$