Question

Simplify: $(2{)}^{\frac{1}{4}}.(4{)}^{\frac{1}{8}}.(8{)}^{\frac{1}{16}}.(16{)}^{\frac{1}{32}}$.

Answer 1

$\left(2{)}^{1/4}\right(4{)}^{1/8}\left(8{)}^{1/16}\right(16{)}^{1/32}$

$=\left(2{)}^{1/4}\right(2^2{)}^{1/8}\left(2^3{)}^{1/16}\right(2^4{)}^{1/32}$

$=\left(2{)}^{1/4}\right(2{)}^{2/8}(2{)}^{3/16}{2}^{4/32}$

$=(2{)}^{1/4+2/8+3/16+4/32}$

$=(2{)}^{\frac{8+8+6+4}{32}}$

$=(2{)}^{26/32}$

$=2^{13/16}$

$Ans{2}^{13/16}$