Question

Question 3(ii)
Find the value of:

$(2^{-1}\times 4^{-1})÷2^{-2}$

Answer 1

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