Question

Find the value of $2^{\frac{2}{3}}\times 2^{\frac{1}{6}}$.

• A. $2^{\frac{5}{6}}$
• B. $2^{\frac{1}{9}}$
• C. $2^{\frac{2}{18}}$
• D. $2^{\frac{1}{6}}$

Answer 1

The correct option is A $2^{\frac{5}{6}}$

$2^{\frac{2}{3}}\times 2^{\frac{1}{6}}$
$\because a^m\times a^m=a^{m+n}$
$\therefore 2^{\frac{2}{3}}\times 2^{\frac{1}{6}}=2^{\frac{2}{3}+\frac{1}{6}}$
$=2^{\frac{4}{6}+\frac{1}{6}}=2^{\frac{5}{6}}$