Question
Using laws of exponents, simplify and write the answer in exponential form:
$\left(5^{21} \div 5^{13}\right) \times 5^7$
$\left(5^{21} \div 5^{13}\right) \times 5^7$
✓
Answer
$\left(5^{21} \div 5^{13}\right) \times 5^7$
We know that,
$a^m \div a^n=a^{m-n} \text { and }\left(a^m \times a^n\right)=(a)^{m+n}$
So, $\left(5^{21} \div 5^{13}\right) \times 5^7=\left(5^{21-13}\right) \times 5^7$
$=\left(5^8\right) \times 5^7$
$=5^{8+7}$
$=5^{15}$
We know that,
$a^m \div a^n=a^{m-n} \text { and }\left(a^m \times a^n\right)=(a)^{m+n}$
So, $\left(5^{21} \div 5^{13}\right) \times 5^7=\left(5^{21-13}\right) \times 5^7$
$=\left(5^8\right) \times 5^7$
$=5^{8+7}$
$=5^{15}$
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