Question

Find the value of each of the following:
(i) ${\left(\frac{1}{2}\right)}^{-1}+{\left(\frac{1}{3}\right)}^{-1}+{\left(\frac{1}{4}\right)}^{-1}$
(ii) ${\left(\frac{1}{2}\right)}^{-2}+{\left(\frac{1}{3}\right)}^{-2}+{\left(\frac{1}{4}\right)}^{-2}$
(iii) (2⁻¹ × 4⁻¹) ÷ 2⁻²
(iv) (5⁻¹ × 2⁻¹) ÷ 6⁻¹

Answer 1

(i)
${\left(\frac{1}{2}\right)}^{-1}+{\left({\displaystyle \frac{1}{3}}\right)}^{-1}+{\left({\displaystyle \frac{1}{4}}\right)}^{-1}=\frac{1}{1/2}+\frac{1}{1/3}+\frac{1}{1/4}$ --> (a⁻¹ = 1/a)
=2+3+4
=12

(ii)
${\left({\displaystyle \frac{1}{2}}\right)}^{-2}+\left({\displaystyle \frac{1}{3}}\right)$^-2+14-2=11/22+11/32+11/42 --> (a⁻ⁿ = 1/(aⁿ))
= $\frac{1}{1/4}+\frac{1}{1/9}+\frac{1}{1/16}$ --> ((a/b)ⁿ = (aⁿ/bⁿ))
= 4+9+16
=29

(iii)
$(2^{-1}\times 4^{-1})÷2^{-2}=\left(\frac{1}{2}\times \frac{1}{4}\right)÷\frac{1}{2^2}$ --> (a⁻ⁿ = 1/(aⁿ))

=$\frac{1}{8}\times 4$
= 2

(iv)
$(5^{-1}\times 2^{-1})÷6^{-1}=\left(\frac{1}{5}\times \frac{1}{2}\right)÷\frac{1}{6}$ --> (a⁻ⁿ = 1/(aⁿ))
$=\frac{1}{10}\times 6$

$=\frac{3}{5}$