Question

I don’t really understand can y’all pls help me

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( 5^{(3)/(2)} \right)^{-(2)/(3)}\implies 5^{-(3)/(2)\cdot (2)/(3)}\implies 5^(-1)\implies \cfrac{1}{5}\implies 0.2 \\\\[-0.35em] ~\dotfill`

`\bf (256^(0.5))^(1.25)\implies [(2^8)^(0.5)]^(1.25)\implies [2^(8\cdot 0.5)]^(1.25)\implies [2^4]^(1.25)\implies 2^(4\cdot 1.25) \\\\\\ 2^5\implies 32 \\\\[-0.35em] ~\dotfill\\\\ ( 81^{-(1)/(6)} )^{(3)/(2)}\implies [(3^4)^{-(1)/(6)} ]^{(3)/(2)}\implies 3^{4\cdot -(1)/(6)\cdot (3)/(2)}\implies 3^{-(12)/(12)}\implies 3^(-1) \\\\\\ \cfrac{1}{3}\implies 0.33...`