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dimulka [17.4K]
3 years ago
10

Simplify ( 8∙4∙2 8∙7 )^2 × ( 8 0 7−3 )^3 × 7 −9 .

Mathematics
1 answer:
stich3 [128]3 years ago
4 0

\bf ~\hspace{7em}\textit{negative exponents}
\\\\
a^{-n} \implies \cfrac{1}{a^n}
~\hspace{4.5em}
a^n\implies \cfrac{1}{a^{-n}}
~\hspace{4.5em}
\cfrac{a^n}{a^m}\implies a^na^{-m}\implies a^{n-m}
\\\\[-0.35em]
\rule{34em}{0.25pt}\\\\
\left( \cfrac{8\cdot 4\cdot 2}{8\cdot 7} \right)^2\times \left( \cfrac{8^0}{7^{-3}} \right)^3\times 7^{-9}\implies \left( \cfrac{8\cdot 8}{8\cdot 7} \right)^2\times \left( \cfrac{1\cdot 7^3}{1} \right)^3\times \cfrac{1}{7^9}


\bf \left( \cfrac{8}{8}\cdot \cfrac{8}{7} \right)^2\times (7^3)^3\times \cfrac{1}{7^9}\implies \left( \cfrac{8}{7} \right)^2\times 7^{3\cdot 3}\times \cfrac{1}{7^9}\implies \cfrac{8^2}{7^2}\times \cfrac{7^9}{7^9}
\\\\\\
\cfrac{8^2}{7^2}\implies \cfrac{64}{49}

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