Simplify and express the following in exponential form: ( a^ 6 a^… - Vidyadip

Question

Simplify and express the following in exponential form: $\Big(\frac{\text{a}^{6}}{\text{a}^{4}}\Big)\times\text{a}^{2}\times\text{a}^{0}$

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Answer

We have, $\Big(\frac{\text{a}^{6}}{\text{a}^{4}}\Big)\times\text{a}^{2}\times\text{a}^{0}$
$=(\text{a}^{6-4}\times\text{a}^{5}\times1)$
$\Big[\because\frac{\text{a}^{\text{m}}}{\text{a}^{\text{n}}}=\text{a}^{\text{m-n}} \text{ and }\text{a}^{0}=1\Big]$
$\text{a}^{2}\times\text{a}^{5}=\text{a}^{2+5}$
$\Big[\because\text{a}^{\text{m}}\times\text{a}^{\text{n}}={\text{a}^{\text{m+n}}}\Big]$
$=\text{a}^{7}$

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