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 ...

`(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.

`(4^4\cdot 4^3)/(4^5)=(4\cdot 4\cdot 4\cdot 4* 4\cdot 4\cdot 4)/(4\cdot 4\cdot 4\cdot 4\cdot 4)\\\\=4\cdot 4=16`