Question

Simplify :

$\frac{\left(2^{2\times 3}\right)\times (2^{3\times 4})}{2^{20}}$ [3 MARKS]

Answer 1

Concept: 1 Mark
Application: 2 Mark

$\frac{\left(2^{2\times 3}\right)\times (2^{3\times 4})}{2^{20}}=\frac{\left(2^6\right)\times (2^{12})}{2^{20}}[a^m\times a^n=a^{mn}]=\frac{\left(2^{6+12}\right)}{2^{20}}=\frac{\left(2^{18}\right)}{2^{20}}=2^{18-20}[a^m÷a^n=a^{m-n}]=2^{-2}=\frac{1}{2^2}=\frac{1}{(2\times 2)}[a^{-m}=\frac{1}{a^m}]=\frac{1}{4}$