Question

The expression $a^{\frac{2}{3}}{\left\{a^{\frac{1}{3}}{\left(a^{\frac{1}{4}}\right)}^4\right\}}^{\frac{1}{4}}$ is equal to

• A. $a^{\frac{1}{2}}$
• B. $a^{\frac{1}{6}}$
• C. a
• D. 1

Answer 1

The correct option is C a

$a^{\frac{2}{3}}{\left\{a^{\frac{1}{3}}{\left(a^{\frac{1}{4}}\right)}^4\right\}}^{\frac{1}{4}}=a^{\frac{2}{3}}{\{a^{\frac{1}{3}}\times a\}}^{\frac{1}{4}}$
= $a^{\frac{2}{3}}{\left(a^{\frac{4}{3}}\right)}^{\frac{1}{4}}=a^{\frac{2}{3}}\times a^{\frac{1}{3}}=a^{\frac{2}{3}+\frac{1}{3}}=a^1=a$