Question 66938
The cube root can be expressed as
*[Tex \Large \sqrt[3]{27x^9y^4z^7}=(27x^9y^4z^7)^{\frac{1}{3}]
Now simply multiply each exponent by 1/3 and take the cube root of 27
*[Tex \Large (27^{\frac{1}{3}}x^{9*\frac{1}{3}}y^{4*\frac{1}{3}}z^{7*\frac{1}{3}})]
So 27 to the one-third power (the cube root of 27) is 3
*[Tex \Large (3x^{\frac{9}{3}}y^{\frac{4}{3}}z^{\frac{7}{3}})]Multiply the exponents
*[Tex \Large (3x^{3}y^{\frac{4}{3}}z^{\frac{7}{3}})]Simplify. There's the simplified expression.
Or it could look like this
*[Tex \Large (3x^{3}\sqrt[3]{y^{4}}\sqrt[3]{z^{7}})]
Either way they are both equal.