Question

What is the simplest form of the product cube root4x^2*cube root8x^7

Answer 1

Answer:

f(x) =  $2^{\frac{5}{3} }x^{3}$ is the simplest expression

Step-by-step explanation:

We are given an expression and we are supposed to find the simplest form of the given expression.

The given expression is

f(x) = $\sqrt[3]{4x^{2} } \times \sqrt[3]{8x^{7} }$

Since the cube root is common we can multiply the quotient inside the radical sign.

f(x) = $\sqrt[3]{32x^{(2+7)} }$

     = $\sqrt[3]{32x^{9} }$

     = $2^{\frac{5}{3} }\times x^{\frac{9}{3} }$

     = $2^{\frac{5}{3} }x^{3}$

f(x) =  $2^{\frac{5}{3} }x^{3}$ is the simplest expression