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Ann [662]
3 years ago
11

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

Mathematics
1 answer:
Umnica [9.8K]3 years ago
5 0
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}
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