Question

Simplify and express each of the following in exponential form: $\frac{(2^3\times 3^4\times 4)}{(3\times 32)}$.

Answer 1

Given: $\frac{(2^3\times 3^4\times 4)}{(3\times 32)}$

Factorization of $32$:

$2\times 2\times 2\times 2\times 2$$=2^5$

Factorization of $4$:

$2\times 2$$=2^2$

On substituting the above values in the given expression we get

$\frac{(2^3\times 3^4\times 2^2)}{(3\times 2^5)}$

$=\frac{(2^{3+2}\times 3^4)}{(3\times 2^5)}$ $[\because a^m\times a^n=a^{m+n}]$

$=\frac{(2^5\times 3^4)}{(3\times 2^5)}$

$=(2^{5-5}\times 3^{4-1})$ $[\because a^m÷a^n=a^{m-n}]$

$=2^0\times 3^3$

$=1\times 3^3$

$=3^3$

$=27$

Therefore, $\frac{(2^3\times 3^4\times 4)}{(3\times 32)}$$=27$.