Question

Michael says that 28%20%7B5%7D%5E%7B3%7D%20%29" id="TexFormula1" title="5( \frac{1}{ {5}^{3} }) = 5 \: ( {5}^{3} )" alt="5( \frac{1}{ {5}^{3} }) = 5 \: ( {5}^{3} )" align="absmiddle" class="latex-formula">is his answer correct? explain

Answer 1

$5\cdot(\frac{1}{5^3})\ne5\cdot(5^3)$

His answer is not correct, when we have a power on the denominator it is dividing and not multiplying, in this case while the expression on the left is being divided the other one is multiplying.

also you could rewrite the expressions like so remembering that powers that are on the denominator can be written as negative powers.

$\begin{gathered} 5\cdot(\frac{1}{5^3})\ne5\cdot(5^3) \\ 5\cdot5^{-3}\ne5^4 \\ 5^{-2}\ne5^4 \end{gathered}$