Question

Express in simplest form : cubed root of a^6b^9/-64. Show work

Answer 1

The answer is  $\frac{ a^{2} b^{3} }{-4}$

$\sqrt[3]{ \frac{ a^{6} b^{9} }{-64} } = \frac{ \sqrt[3]{a^{6} b^{9}} }{ \sqrt[3]{-64} } = \frac{ \sqrt[3]{a^{6}} * \sqrt[3]{ b^{9}} }{ \sqrt[3]{-64}}$
Since (xᵃ)ᵇ = xᵃ*ᵇ, then:
a⁶ = (a²)³
b⁹ = (b³)³
Also: 64 = 4³
$\frac{ \sqrt[3]{a^{6}} * \sqrt[3]{ b^{9}} }{ \sqrt[3]{-64}}= \frac{ \sqrt[3]{( a^{2})^{3} }*\sqrt[3]{( b^{3})^{3} } }{\sqrt[3]{( -4)^{3} }} = \frac{ a^{2} * b^{3} }{-4}$