$\displaystyle
Write$ $\displaystyle in$ $\displaystyle simplest$ $\displaystyle index$ $\displaystyle notation.$
$\displaystyle
\frac{8\times5^2}{2^3\times10}
$
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Hello, Mr Rayon!
Not sure what "index notation" means.$\displaystyle \text{Write in simplest index notation: }\;\frac{8\cdot5^2}{2^3\cdot10} $
. . I assume it means "with exponents."
The problem is just arithmetic, isn't it?
We have: .$\displaystyle \frac{8\cdot5^2}{2^3\cdot10} \:=\:\frac{200}{80} \;=\;\frac{5}{2} \;=\;2^{-1}\!\cdot5$
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If we have to use exponents . . .
. . $\displaystyle \frac{8\cdot5^2}{2^3\cdot10} \;=\;\frac{2^3\cdot 5^2}{2^3\cdot(2\cdot5)} \;=\;\frac{2^3}{2^4}\cdot\frac{5^2}{5} \;=\;2^{-1}\!\cdot5 $