Simplify radical using the exponent rule. Show work

Question

asked Jun 8, 2020 37.1k views

1 Answer

Kankaristo · Answer 1 · 2020-06-14T10:33:53+0000

Answer:

(1)/(x^(4) )

Explanation:

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

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

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

rewrite both terms:

(
$x^{(2)/(3) }$ ×
$x^{(4)/(6) }$ )⁻³

simplify the 4/6:

(
$x^{(2)/(3) }$ ×
$x^{(2)/(3) }$ )⁻³

bases are the same, add the exponents:

(
$x^{(4)/(3) }$ )⁻³

multiply the exponents:

$x^{(-12)/(3) }$

simplify:

x⁻⁴

negative power rule:

(1)/(x^(4) )