Question

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

Answer 1

`\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* \left( \cfrac{8^0}{7^(-3)} \right)^3* 7^(-9)\implies \left( \cfrac{8\cdot 8}{8\cdot 7} \right)^2* \left( \cfrac{1\cdot 7^3}{1} \right)^3* \cfrac{1}{7^9}`

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