Select the equivalent expression. root(6)((k^(6))/(k^(4))) k^(-(1)/(3)) k^(-3) k^(3) k^((1)/(3))

Simplify Inside Sixth Root: Simplify the expression inside the sixth root. We have the expression root(6)((k^(6))/(k^(4))). To simplify the expression inside the root, we use the property of exponents that states when dividing like bases, we subtract the exponents. So, (k^(6))/(k^(4)) = k^(6-4) = k^(2).Apply Sixth Root: Apply the sixth root to the simplified expression. Now we apply the sixth root to k^(2), which can be written as (k^(2))^(1/6). Using the property of exponents (a^(m))^n = a^(m*n), we multiply the exponents. So, (k^(2))^(1/6) = k^(2*(1/6)) = k^(2/6).Simplify Exponent: Simplify the exponent. We simplify the fraction 2/6 by dividing both the numerator and the denominator by their greatest common divisor, which is 2. So, k^(2/6) simplifies to k^(1/3).

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Select the equivalent expression.

root(6)((k^(6))/(k^(4)))

k^(-(1)/(3))

k^(-3)

k^(3)

k^((1)/(3))

Select the equivalent expression. $\newline$ $\sqrt[6]{\frac{k^{6}}{k^{4}}}$ $\newline$ $k^{-\frac{1}{3}}$ $\newline$ $k^{-3}$ $\newline$ $k^{3}$ $\newline$ $k^{\frac{1}{3}}$

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Math Problems

Algebra 1

Multiplication with rational exponents

Full solution

Q. Select the equivalent expression.

\newline

\sqrt[6]{\frac{k^{6}}{k^{4}}}

\newline

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

\newline

k^{-3}

\newline

k^{3}

\newline

k^{\frac{1}{3}}

Simplify Inside Sixth Root: Simplify the expression inside the sixth root. $\newline$ We have the expression $\sqrt[6]{\frac{k^{6}}{k^{4}}}$ . To simplify the expression inside the root, we use the property of exponents that states when dividing like bases, we subtract the exponents. $\newline$ So, $\frac{k^{6}}{k^{4}} = k^{6-4} = k^{2}$ .
Apply Sixth Root: Apply the sixth root to the simplified expression. $\newline$ Now we apply the sixth root to $k^{2}$ , which can be written as $(k^{2})^{\frac{1}{6}}$ . $\newline$ Using the property of exponents $(a^{m})^{n} = a^{m*n}$ , we multiply the exponents. $\newline$ So, $(k^{2})^{\frac{1}{6}} = k^{2*\frac{1}{6}} = k^{\frac{2}{6}}$ .
Simplify Exponent: Simplify the exponent. $\newline$ We simplify the fraction $\frac{2}{6}$ by dividing both the numerator and the denominator by their greatest common divisor, which is $2$ . $\newline$ So, $k^{\frac{2}{6}}$ simplifies to $k^{\frac{1}{3}}$ .