Simplify and express each of the following in exponential form:
$({(5^{2})}^{3} \times 5^{4}) \div 5^{7}$

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Solution

$\begin{matrix} ({(5^{2})}^{3} \times 5^{4}) \div 5^{7} = (5^{6} \times 5^{4}) \div 5^{7} [{(a^{m})}^{n} = a^{m n}] = 5^{10} \div 5^{7} [a^{m} \times a^{n} = a^{m + n}] = 5^{10 - 7} [\frac{a^{m}}{a^{n}} = a^{m - n}] = 5^{3} = 125 \end{matrix}$

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Question 84 (e)

Simplify and express each of the following in exponential form.
$[{(\frac{3}{5})}^{3} \times {(\frac{3}{5})}^{8}] \div [{(\frac{3}{5})}^{2} \times {(\frac{3}{5})}^{4}]$

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Simplify and express each of the following in exponential form:((52)3×54)÷57

((52)3×54)÷57=(56×54)÷57[(am)n=amn]=510÷57[am×an=am+n]=510−7[aman=am−n]=53=125

Simplify and express each of the following in exponential form:
$({(5^{2})}^{3} \times 5^{4}) \div 5^{7}$

$\begin{matrix} ({(5^{2})}^{3} \times 5^{4}) \div 5^{7} = (5^{6} \times 5^{4}) \div 5^{7} [{(a^{m})}^{n} = a^{m n}] = 5^{10} \div 5^{7} [a^{m} \times a^{n} = a^{m + n}] = 5^{10 - 7} [\frac{a^{m}}{a^{n}} = a^{m - n}] = 5^{3} = 125 \end{matrix}$