Rewrite expressions with radicals and rational exponents using exponent properties.
Simplify a product of like bases by adding rational exponents
Problem
Simplify \(a^{2/3}\cdot~a^{1/3}\) using the product rule for equal bases. Add the exponents and reduce the resulting power.
Big Picture
What this problem is really about
The product rule for equal bases combines factors by adding their exponents. We’ll keep the common base, add the two rational numbers with their shared denominator, reduce the sum, and simplify the resulting power. Expanding that compact form back into the original two factors verifies the exponent arithmetic without evaluating the variable.
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