Question

Which of the following 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 ${\left(y^{\frac{1}{3}}\right)}^{12}$

Let's consider option (a),
${\left(y^{\frac{2}{3}}\right)}^9=y^{\frac{2}{3}\times 9}[\because (x^m{)}^n=x^{m\times n}]=y^6$
Let's consider option (b),
${\left(\sqrt{y^6}\right)}^2=\left(\right(y^6{)}^{\frac{1}{2}}{)}^2[\because \sqrt{x}=x^{\frac{1}{2}}]=(y^6{)}^{\frac{1}{2}\times 2}=y^6$
Let's consider option (c),
$\sqrt[3]{3y^{18}}=\left(y^{18}{)}^{\frac{1}{3}}\right[\because \sqrt{x}=x^{\frac{1}{2}}]=y^{(18\times \frac{1}{3})}[\because (x^m{)}^n=x^{m\times n}]=y^6$
Let's now consider option (d),
${\left(y^{\frac{1}{3}}\right)}^{1}2=y^{\frac{2}{3}\times 12}[\because (x^m{)}^n=x^{m\times n}]=y^8$
Option d is correct.