Evaluate (5/6)^(-3): Negative Exponent Expression Solution

The negative exponent rule $x^{-n} = \frac{1}{x^n}$ means "take the reciprocal and make the exponent positive." For fractions, the reciprocal of $\frac{5}{6}$ is $\frac{6}{5}$ - you flip it!

They're actually the same value mathematically, but $\left(\frac{6}{5}\right)^{3}$ is the simplified form we want. The negative exponent applies to the whole fraction, not separately to numerator and denominator.

Not for this type of problem! The question asks for the equivalent expression, so $\left(\frac{6}{5}\right)^{3}$ is the complete answer. You don't need to compute $\frac{216}{125}$.

Think of it as "undoing" the negative: negative exponent means "flip and make positive." So $\left(\frac{5}{6}\right)^{-3}$ becomes $\left(\frac{6}{5}\right)^{3}$ - flip the fraction, flip the sign!

Then you wouldn't need to flip anything! $\left(\frac{5}{6}\right)^{3}$ would stay as $\left(\frac{5}{6}\right)^{3}$. The negative exponent is what triggers the reciprocal rule.