Rewrite expressions with radicals and rational exponents using exponent properties.
Choose a form by an explicit direct-operation criterion
Problem
Evaluate \(81^{3/4}\) mentally using a form that exposes a direct first operation. State the form, the operation performed first, and the value.
Big Picture
What this problem is really about
The most useful form is the one that exposes an exact first operation. We’ll read the denominator as a root index and numerator as a power, rewrite the expression so the perfect root is visible, perform that root first, and then apply the remaining integer power.
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