Question

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

[2 Marks]

Answer 1

$\frac{2^3\times 3^4\times 4}{3\times 32}=\frac{2^3\times 3^4\times 2^2}{3\times 2^5}=\frac{2^{3+2}\times 3^4}{3\times 2^5}[\because a^m\times a^n=a^{m+n}]$

[1 Mark]
$=\frac{2^5\times 3^4}{3\times 2^5}=2^{5-5}\times 3^{4-1}[\because a^m÷a^n=a^{m-n}]$
$=2^0\times 3^3=1\times 3^3=3^3$

[1 Mark]