Question
Simplify and express in exponential form: $\frac{2^{3} \times 3^{4} \times 4}{3 \times 32}$
✓
Answer
In the above question,
We have to simplify the given numbers into exponential form:
Therefore, We have,
$\frac{2^{2} \times 3^{4} \times 4}{3 \times 32}=\frac{2^{3} \times 3^{4} \times 2 \times 2}{3 \times 2 \times 2 \times 2 \times 2 \times 2}$ = $\frac{2^{3} \times 3^{4} \times 2^{2}}{3 \times 2^{5}}$ = $\frac{2^{3} \times 2^{2} \times 3^{4}}{3 \times 2^{5}}$
$=\frac{2^{5} \times 3^{4}}{3 \times 2^{5}}\left(a^{m} \times a^{n}=a^{m+n}\right)$
Using identity: $\left(a^m \div a^n=a^{m-n}\right)$
$=2^{5-5} \times 3^{4-1}$
$=2^0 3^3$
$=1 \times 3^3$
$=3^3$
We have to simplify the given numbers into exponential form:
Therefore, We have,
$\frac{2^{2} \times 3^{4} \times 4}{3 \times 32}=\frac{2^{3} \times 3^{4} \times 2 \times 2}{3 \times 2 \times 2 \times 2 \times 2 \times 2}$ = $\frac{2^{3} \times 3^{4} \times 2^{2}}{3 \times 2^{5}}$ = $\frac{2^{3} \times 2^{2} \times 3^{4}}{3 \times 2^{5}}$
$=\frac{2^{5} \times 3^{4}}{3 \times 2^{5}}\left(a^{m} \times a^{n}=a^{m+n}\right)$
Using identity: $\left(a^m \div a^n=a^{m-n}\right)$
$=2^{5-5} \times 3^{4-1}$
$=2^0 3^3$
$=1 \times 3^3$
$=3^3$
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