Simplify and express in exponential form: [ (5^ 2 )^ 3 5^ 4 ] 5^ … - Vidyadip

Question

Simplify and express in exponential form: $\left[\left(5^{2}\right)^{3} \times 5^{4}\right] \div 5^{7}$

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Answer

In the above question,
We have to simplify the given numbers into exponential form:
$\left[\left(5^2\right)^3 \times 5^4\right] \div 5^7$
Using identity: $\left.\left(a^m\right)^n=a^{m n}\right)$
$=\left[(5)^2 \times 3 \times 5^4\right] \div 5^7$
$=\left[(5)^6 \times 4\right] \div 5^7$
Using identity: ( $a^m \times a^n=a^{m+n}$ )
$=\left[5^{6+4}\right] \div 5^7$
Using identity: ( $\left.a^m \div a^n=a^{m-n}\right)$
Therefore,
$=5^{10} \div 5^7$
$=5^{10-7}=5^3$

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