Question

Simplify radical using the exponent rule. Show work

Answer 1

Answer:

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

Step-by-step explanation:

($\sqrt[3]{x^{2} }$ × $\sqrt[6]{x^{4}}$)⁻³

$\sqrt[3]{x^{2} }$ is the same thing as $x^{\frac{2}{3} }$

you can think of the numerator as the power and the denominator as the root

rewrite both terms:

($x^{\frac{2}{3} }$ × $x^{\frac{4}{6} }$)⁻³

simplify the 4/6:

($x^{\frac{2}{3} }$ × $x^{\frac{2}{3} }$)⁻³

bases are the same, add the exponents:

($x^{\frac{4}{3} }$)⁻³

multiply the exponents:

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

simplify:

x⁻⁴

negative power rule:

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