Question

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

Answer 1

The answer is
`( a^(2) b^(3) )/(-4)`


`\sqrt[3]{ ( 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) }} = ( a^(2) * b^(3) )/(-4)`