Rewrite expressions with radicals and rational exponents using exponent properties.
Simplify a product of like bases by adding rational exponents
Problem
For \(x\ge~0\), simplify \(x^{1/2}\cdot~x^{3/2}\) by adding the exponents on the common base. Preserve the stated domain in the result.
Big Picture
What this problem is really about
Multiplying powers with the same base means adding their exponents, including fractional ones. We’ll keep the base, add the rational exponents with their common denominator, simplify the sum, and carry the stated real-domain condition into the final equivalent expression.
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