Question
Simplify and express the following in exponential form:
$\left(5^{15} \div 5^{10}\right) \times 5^5$
$\left(5^{15} \div 5^{10}\right) \times 5^5$
✓
Answer
We have, $(5^{15} \div 5^{10}) \times 5^{5}\Big(\frac{5^{15}}{5^{10}}\Big)\times5^{5}$$=5^{15-10}\times5^{5}$
$5^{5}=5^{15-10}\times5^{5}$ $\Big[\because\frac{\text{a}^{\text{m}}}{\text{a}^{\text{n}}}=\text{a}^{\text{m-n}}\Big]$
$$ $=5^{5}\times5^{5}=5^{5+5}=5^{10}$ $\Big[\because\text{a}^{\text{m}}\times\text{a}^{\text{n}}={\text{a}^{\text{m+n}}}\Big]$
$5^{5}=5^{15-10}\times5^{5}$ $\Big[\because\frac{\text{a}^{\text{m}}}{\text{a}^{\text{n}}}=\text{a}^{\text{m-n}}\Big]$
$$ $=5^{5}\times5^{5}=5^{5+5}=5^{10}$ $\Big[\because\text{a}^{\text{m}}\times\text{a}^{\text{n}}={\text{a}^{\text{m+n}}}\Big]$
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