Question
Simplify and express the following in exponential form: $\Bigg[\Big(\frac{7}{11}\Big)^{5}\div\Big(\frac{7}{11}\Big)^{2}\Bigg]\times\Big(\frac{7}{11}\Big)^{2}$
✓
Answer
We have, $\Bigg[\Big(\frac{7}{11}\Big)^{5}\div\Big(\frac{7}{11}\Big)^{2}\Bigg]\times\Big(\frac{7}{11}\Big)^{2}$
$=\Bigg[\frac{\Big(\frac{7}{11}\Big)^{5}}{\Big(\frac{7}{11}\Big)^{2}}\Bigg]\times\Big(\frac{7}{11}\Big)^{2}=\Big(\frac{7}{11}\Big)^{5-2}\times\Big(\frac{7}{11}\Big)^{2}$
$\Big[\because\frac{\text{a}^{\text{m}}}{\text{a}^{\text{n}}}=\text{a}^{\text{m-n}}\Big]$
$=\Big(\frac{7}{11}\Big)^{3}\times\Big(\frac{7}{11}\Big)^{2}$
$\Big[\because \text{a}^{\text{m}}\times \text{a}^{\text{n}}=\text{a}^{\text{m-n}}\Big]$
$=\Big(\frac{7}{11}\Big)^{3+2}=\Big(\frac{7}{11}\Big)^{5}$
$=\Bigg[\frac{\Big(\frac{7}{11}\Big)^{5}}{\Big(\frac{7}{11}\Big)^{2}}\Bigg]\times\Big(\frac{7}{11}\Big)^{2}=\Big(\frac{7}{11}\Big)^{5-2}\times\Big(\frac{7}{11}\Big)^{2}$
$\Big[\because\frac{\text{a}^{\text{m}}}{\text{a}^{\text{n}}}=\text{a}^{\text{m-n}}\Big]$
$=\Big(\frac{7}{11}\Big)^{3}\times\Big(\frac{7}{11}\Big)^{2}$
$\Big[\because \text{a}^{\text{m}}\times \text{a}^{\text{n}}=\text{a}^{\text{m-n}}\Big]$
$=\Big(\frac{7}{11}\Big)^{3+2}=\Big(\frac{7}{11}\Big)^{5}$
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