Question

$4^{-2}+4^{-1}+4^0+4^2$ = _____.
A. $\frac{277}{16}$

B. $\frac{277}{18}$

C. $\frac{257}{16}$

D. $\frac{271}{18}$

[1 mark]

Answer 1

Note that $a^0=1$ for any non-zero integer $a$.
Also, for integers $a$ and $m(\ne 0)$
$a^{-m}=\frac{1}{a^m}.$
$⟹4^{-2}=\frac{1}{4^2}=\frac{1}{16}$ and $4^{-1}=\frac{1}{4^1}$
$\therefore 4^{-2}+4^{-1}+4^0+4^2=\frac{1}{16}+\frac{1}{4}+1+16$
$=\frac{1+4+16+256}{16}$
$=\frac{277}{16}$
Hence option A is correct.
[1 mark]