Simplify cube root of 1/(k^-2*k)

$\sqrt[3]{\frac{1}{k^{- 2} \cdot k}}$

Step 1

Multiply $k^{- 2}$ by $k$ by adding the exponents.

Multiply $k^{- 2}$ by $k$ .

Raise $k$ to the power of $1$ .

$\sqrt[3]{\frac{1}{k^{- 2} \cdot k^{1}}}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\sqrt[3]{\frac{1}{k^{- 2 + 1}}}$

Add $- 2$ and $1$ .

$\sqrt[3]{\frac{1}{k^{- 1}}}$

Step 2

Move $k^{- 1}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\sqrt[3]{k}$