Question

If ${64}^a=\frac{1}{{256}^b}$, then $3a+4b$ equals:

• A. $2$
• B. $4$
• C. $8$
• D. $0$

Answer 1

The correct option is D $0$

${64}^a=\frac{1}{{256}^b}$
$\Rightarrow (2^6{)}^a=\frac{1}{(2^8{)}^b}$
$\Rightarrow 2^{6a}\times 2^{8b}=1$
$\Rightarrow 2^{6a+8b}=2^0$
$\Rightarrow 6a+8b=0$
$\Rightarrow 3a+4b=0$