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AVprozaik [17]
2 years ago
5

Please solve this law of indices​

Mathematics
2 answers:
PilotLPTM [1.2K]2 years ago
5 0

4√36^-1 = 36^-1/4

36^3/4 • 36^-1/4

=36^2/4

or √36 = 6

Ludmilka [50]2 years ago
5 0

\sf Formulas:  \displaystyle \\\\\ 1)  \ a^{n} \cdot a^{m}=a^{n+m}  \\\\ 2) \sf \ \sqrt[n]{\sf a^{m}} = a^{\tfrac{m}{n} }  \\\\\\ Solution : \\\\\\\sf \large \boldsymbol {}  \displaystyle (36)^{\tfrac{3}{4} } \cdot \sqrt[\sf 4 ]{\sf 36^{-1}} }= 36^{\tfrac{3}{4} } \cdot 36^{\tfrac{-1}{4} } =36^{\tfrac{3}{4}+\big(-\tfrac{1}{4} \big ) }= \\\\\\\ 36^{\tfrac{3}{4} -\tfrac{1}{4}  } =36^{\tfrac{2}{4} }=(6^ {\backslash \!\!\!2})^{\tfrac{1}{\backslash\!\!\!2} }= 6^1=\boxed{\sf 6}

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