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Simplify the following:
\( \frac{\left(4 \times 10^{7}\right)\left(6 \times 10^{-5}\right)}{8 \times 10^{4}} \)
Given:
\( \frac{\left(4 \times 10^{7}\right)\left(6 \times 10^{-5}\right)}{8 \times 10^{4}} \)
To do:
We have to simplify the given expression.
Solution:
We know that,
$(a^{m})^{n}=a^{m n}$
$a^{m} \times a^{n}=a^{m+n}$
$a^{m} \div a^{n}=a^{m-n}$
$a^{0}=1$
Therefore,
$\frac{(4 \times 10^{7})(6 \times 10^{-5})}{8 \times 10^{4}}=\frac{4 \times 6}{8}\times 10^{(7-5-4)}$
$=3 \times 10^{-2}$
$=\frac{3}{10^{2}}$
$=\frac{3}{100}$
Hence, $\frac{(4 \times 10^{7})(6 \times 10^{-5})}{8 \times 10^{4}}=\frac{3}{100}$.
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