Question

I have this grade 9 fractions question, please help (-4•1/2)^2 (25/4)^2

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}`

`\bf \left( -4\cdot \cfrac{1}{2} \right)^2\left( \cfrac{25}{4} \right)^2\implies \stackrel{\mathbb{PEMDAS}}{\left( -2 \right)^2\left( \cfrac{25^2}{4^2} \right)}\implies (-2)(-2)\cdot \cfrac{625}{(2^2)^2}\implies 2^2\cdot \cfrac{625}{2^(2\cdot 2)} \\\\\\ \cfrac{2^2\cdot 625}{2^4}\implies \cfrac{625}{2^(-2)\cdot 2^4}\implies \cfrac{625}{2^(-2+4)}\implies \cfrac{625}{2^2}\implies \cfrac{625}{4}\implies 156(1)/(4)`