Question

4 to the 4th power times 4 to the 3rd power over 4 to the 5th power

Answer 1

$\bf ~\hspace{7em}\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^{-n}} ~\hspace{4.5em} \cfrac{a^n}{a^m}\implies a^na^{-m}\implies a^{n-m} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \cfrac{4^4\cdot 4^3}{4^5}\implies \cfrac{4^{4+3}}{4^5}\implies \cfrac{4^7}{4^5}\implies \cfrac{4^7\cdot 4^{-5}}{1}\implies 4^{7-5}\implies 4^2\implies 16$

Answer 2

By the laws of exponents ...

$\dfrac{4^4\cdot 4^3}{4^5}=4^{(4+3-5)}\\\\=4^2=16$

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If what you want is the value, your calculator can deliver.

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Or, you can recognize that an exponent signfies repeated multiplication.

$\dfrac{4^4\cdot 4^3}{4^5}=\dfrac{4\cdot 4\cdot 4\cdot 4\times 4\cdot 4\cdot 4}{4\cdot 4\cdot 4\cdot 4\cdot 4}\\\\=4\cdot 4=16$