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: -8, -2

Step-by-step explanation: (the previous answers are ) 1. D 2. C 3. -8,-2 (for reference of order :))

Answer 2

`a = 2`

`b = 2^(1/6)`

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)`