Question

The value of ∛x^10, when x = -2, can be written in simplest form as a∛b, where a = ___ and b = ___.

Answer 1

Person above me is right

Explanation:

Answer 2

a = -8

b = -2

Explanation:

We have been given the following radical expression;

`\sqrt[3]{x^(10) }`

The radical can be expressed using the law of exponents;

`\sqrt[n]{x}=x^{(1)/(n) }`

The radical can thus be re-written as;

`\sqrt[3]{x^(10) }=(x^(10))^{(1)/(3) }`

Using the law of exponents;

`(a^(b))^(c)=a^(bc)`

The last expression becomes;

`(x^(10))^{(1)/(3) }=x^{(10)/(3) }=x^(3)*x^{(1)/(3) }\\\\=x^(3)\sqrt[3]{x}`

substituting x with -2 yields;

`-2^(3)\sqrt[3]{-2}=-8\sqrt[3]{-2}`