Question

If x≠0, which expression is equivalent to this expression? x3√4x112

Answer 1

Answer:

$x^{\frac{2}{3}}$

Step-by-step explanation:

Given:

$\frac{\sqrt[4]{x^3}}{x^{\frac{1}{12}}}$

Required:

Equivalent expression of the above expression if x ≠ 0

Solution:

$\frac{\sqrt[4]{x^3}}{x^{\frac{1}{12}}}$

Applying lower rule of exponents, rewrite the numerator

$\frac{x^{\frac{3}{4}}}{x^{\frac{1}{12}}}$

Next, apply the Quotient rule of exponents

$x^{\frac{3}{4} - \frac{1}{12}}$

$x^{\frac{9 - 1}{12}}$

$x^{\frac{8}{12}}$

$x^{\frac{2}{3}}$