Question

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

Answer 1

f(x) =
`2^{(5)/(3) }x^(3)` is the simplest expression

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) } * \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^{(5)/(3) }* x^{(9)/(3) }`

=
`2^{(5)/(3) }x^(3)`

f(x) =
`2^{(5)/(3) }x^(3)` is the simplest expression