Question

Question 3(iii)
Find the value of:

${\left(\frac{1}{2}\right)}^{-2}+{\left(\frac{1}{3}\right)}^{-2}+{\left(\frac{1}{4}\right)}^{-2}$

Answer 1

${\left(\frac{1}{2}\right)}^{-2}+{\left(\frac{1}{3}\right)}^{-2}+{\left(\frac{1}{4}\right)}^{-2}=(2^{-1}{)}^{-2}+(3^{-1}{)}^{-2}+(4^{-1}{)}^{-2}[\because a^{-m}=\frac{1}{a^m}]=2^{\left(2\right)}+3^{\left(2\right)}+4^{\left(2\right)}[\because (a^m{)}^n=a^{m\times n}]=2^2+3^2+4^2=4+9+16=29$