Simplifying with square roots?

[arroww]

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

\(\displaystyle 3\sqrt{\frac{(10x^3)^2}{(10x^6)^{-1}}}\)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: .$$\sqrt[3]{10^3x^{12}} \;=\;\left(10^3x^{12}\right)^{\frac{1}{3}}$$

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