Rewrite expressions with radicals and rational exponents using exponent properties.
Rewrite a product of radicals with the same base by adding rational exponents
Problem
Rewrite \(\sqrt{x}\cdot~\sqrt[3]{x}\) as \(x^{1/2}\cdot~x^{1/3}\), then add the exponents using a common denominator.
Big Picture
What this problem is really about
Radicals with the same radicand become like-base powers after conversion to rational exponents. We’ll translate each root index, add the exponents with a common denominator, reduce the sum, and preserve the nonnegative real domain imposed by the original square root.
Inside Gozunta
Turn the preview into practice.
More than a preview
Gozunta lets you study this problem—and more than 10,000 others.
Create targeted learning sessions, use hints, check your answer, read the walkthrough, watch the video, print the work, and track your progress.
