Question

Which of the following is not equal to $y^6$?

• A. ${\left(y^{\frac{2}{3}}\right)}^9$
• B. ${\left(\sqrt{y^6}\right)}^2$
• C. $\sqrt[3]{3y^{18}}$
• D. ${\left(y^{\frac{1}{3}}\right)}^{12}$

Answer 1

The correct option is D

${\left(y^{\frac{1}{3}}\right)}^{12}$

${\left(y^{\frac{1}{3}}\right)}^{12}$
$=y^{\frac{1}{3}\times 12}=y^4\ne y^6$
But,
(1) : ${\left(y^{\frac{2}{3}}\right)}^9=y^{\frac{2}{3}\times 9}=y^6$
(2) : ${\left(\sqrt{y^6}\right)}^2=y^6$
(3) : $\sqrt[3]{3y^{18}}=(y^{18}{)}^{\frac{1}{3}}=y^6$