Question:

If \(x=\left(\dfrac{3}{2}\right)^{-2}\div\left(\dfrac{2}{3}\right)^{-4}\), the value of \(x^{2}\) is

Show Hint

Division of like bases $\Rightarrow$ subtract exponents; negative power inverts the base.
Updated On: Aug 11, 2025
  • $\left(\dfrac{2}{3}\right)^{12}$
  • $\left(\dfrac{3}{2}\right)^{-12}$
  • $\left(\dfrac{6}{5}\right)^{-12}$
  • $\left(\dfrac{5}{6}\right)^{-12}$
Hide Solution
collegedunia
Verified By Collegedunia

The Correct Option is A

Solution and Explanation

$x=\left(\dfrac{3}{2}\right)^{-2}\div\left(\dfrac{2}{3}\right)^{-4} =\left(\dfrac{3}{2}\right)^{-2}\times\left(\dfrac{3}{2}\right)^{-4} =\left(\dfrac{3}{2}\right)^{-6}$.
Therefore $x^{2}=\left(\dfrac{3}{2}\right)^{-12}=\left(\dfrac{2}{3}\right)^{12}$.
Was this answer helpful?
0
0

Questions Asked in CLAT exam

View More Questions