Question

The value of cube root of x^10, when x = -2, can be written in simplest form as a^3 times the square root of b, where a = _____ and b = ______.

Answer 1

Answer:

$a = 2$

$b = 2^{1/6}$

Step-by-step explanation:

Given

$\sqrt[3]{x^{10}} = a^3 * \sqrt b$

$x = -2$

Required

Find a and b

We have:

$\sqrt[3]{x^{10}} = a^3 * \sqrt b$

Substitute -2 for x

$\sqrt[3]{(-2)^{10}} = a^3 * \sqrt b$

$\sqrt[3]{1024} = a^3 * \sqrt b$

Expand

$\sqrt[3]{2^9 * 2} = a^3 * \sqrt b$

Split the exponents

$2^{(9/3)} * 2^{(1/3)} = a^3 * \sqrt b$

$2^{3} * 2^{1/3} = a^3 * \sqrt b$

By comparison:

$a^3 = 2^3$

So;

$a = 2$

and

$\sqrt b = 2^{1/3}$

Take square roots of both sides

$b = 2^{1/6}$