Question

What is the following product? Assume x>/=0 ^3sqrt(x^2)*^sqrtx^3

Answer 1

Answer:

$x(\sqrt[12]{x^5} )$

Step-by-step explanation:

We need to remember 2 rules when doing these:

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

2. $x^a*x^b=x^{ab}$

Using these 2 rules, we can simplify the product (steps shown below):

$\sqrt[3]{x^2} *\sqrt[4]{x^3} \\=x^{\frac{2}{3}}*x^{\frac{3}{4}}\\=x^{\frac{2}{3}+\frac{3}{4}}\\=x^{\frac{17}{12}}\\=x^{\frac{12}{12}+\frac{5}{12}}\\=x(x^{\frac{5}{12}})\\=x(\sqrt[12]{x^5} )$

Rearranging, we see that it is the third choice.