MHB Simplifying with square roots?

[arroww]

So, this is probably really simple...but I keep getting the wrong answer when trying to simplify this:

$$3\sqrt{\frac{(10x^3)^2}{(10x^6)^{-1}}}$$Could someone show the steps to simplifying it? Thanks so much. (:

 

[soroban]

Hello, arroww!

\sqrt[3]{\frac{(10x^3)^2}{(10x^6)^{\text{-}1}}}

Under the cube root, we have:

.\frac{(10x^3)^2}{(10x^6)^{\text{-}1}} \;=\; (10x^3)^2(10x^6)^1

. . . =\;10^2\cdot x^6\cdot 10\cdot x^6 \;=\;10^3x^{12}

Then: .\sqrt[3]{10^3x^{12}} \;=\;\left(10^3x^{12}\right)^{\frac{1}{3}}

. . . =\;\left(10^3\right)^{\frac{1}{3}}\left(x^{12} \right)^{\frac{1}{3}} \;=\;10x^4