Question

Mark (✓) against the correct answer

(2⁻¹ − 4⁻¹)² = ?

(a) 4
(b) −4
(c) $\frac{1}{16}$
(d) $\frac{-1}{16}$

Answer 1

(c) $\frac{1}{16}$

We have:

${\left(2^{-1}-4^{-1}\right)}^2={\left(\frac{1}{2}-\frac{1}{4}\right)}^2$
= ${\left(\frac{2-1}{4}\right)}^2$ [since L.C.M. of 2 and 4 is 4]
= ${\left(\frac{1}{4}\right)}^2$
= $\left(\frac{1}{4}\times \frac{1}{4}\right)=\frac{1}{16}$