Question

Find the value of $2^{\frac{1}{4}}.4^{\frac{1}{8}}.{16}^{\frac{1}{16}}.{256}^{\frac{1}{32}}$

• A. $1$
• B. $2$
• C. $3$
• D. $8$

Answer 1

Answer: (B)

$2$

Lets rewrite with common base as we know that $x^a\times x^b=x^{a+b}$.

$2^{1/4}\times 2^{2/8}\times 2^{4/16}\times 2^{8/32}$

$=2^{\left(1/4\right)+\left(1/4\right)+\left(1/4\right)+\left(1/4\right)}$

$=2^{4\times 1/4}=2^1=2$