Question

NEED HELP PLEASE
What is the simplified version of sqrt p^7

Answer 1

We use two index laws and combine them, the power of a power rule and the sqrt as a fractional index of half
\[(a^m)^n = a^{mn}\]
\[\sqrt a = a^{\frac{ 1 }{ 2 }}\]

\[\sqrt{ a^7} = (a^7)^{\frac{ 1 }{ 2 }} = a^{ \frac{ 7 }{ 2 }}\]

General rule (fractional indices)

\[a^\frac{ m }{ n } = (a^m)^\frac{ 1 }{ n } = \sqrt[n]{a^m} ~OR~ (\sqrt[n]{a})^m\]

Answer 2

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Answer 3

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