Q.Simplify: $\left(\dfrac{4}{9}\right)^{-1/2}$.

A negative exponent first flips the fraction; the remaining fractional exponent is then a square root.

Flip: $\left(\dfrac{9}{4}\right)^{1/2}=\sqrt{\dfrac{9}{4}}=\dfrac{3}{2}$.

Step 1 — apply the negative-exponent law (take the reciprocal, drop the negative sign):

Step 2 — apply the fractional-exponent law (square root, distributing to numerator and denominator):

Check (independent recomputation): verify by squaring the answer and comparing to the reciprocal fraction — $\left(\dfrac32\right)^2=\dfrac94$, and $\dfrac94$ is exactly the reciprocal of $\dfrac49$ ✓.

Forgetting to flip the fraction when handling the negative exponent (attempting to take the square root of $4/9$ directly and then guessing a sign), or flipping the fraction but then forgetting to also take the square root afterward.