Question

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

Answer 1

Answer:

a = -8

b = -2

Step-by-step explanation:

We have been given the following radical expression;

$\sqrt[3]{x^{10} }$

The radical can be expressed using the law of exponents;

$\sqrt[n]{x}=x^{\frac{1}{n} }$

The radical can thus be re-written as;

$\sqrt[3]{x^{10} }=(x^{10})^{\frac{1}{3} }$

Using the law of exponents;

$(a^{b})^{c}=a^{bc}$

The last expression becomes;

$(x^{10})^{\frac{1}{3} }=x^{\frac{10}{3} }=x^{3}*x^{\frac{1}{3} }\\\\=x^{3}\sqrt[3]{x}$

substituting x with -2 yields;

$-2^{3}\sqrt[3]{-2}=-8\sqrt[3]{-2}$