Rewrite expressions with radicals and rational exponents using exponent properties.
Simplify a quotient with rational exponents by subtracting exponents
Problem
For \(x\ne~0\), simplify \(x^{5/3}/x^{2/3}\) with the quotient rule. Subtract the denominator exponent from the numerator exponent and reduce fully.
Big Picture
What this problem is really about
Dividing powers with the same nonzero base subtracts the denominator exponent from the numerator exponent. We’ll keep that order, simplify the fractional difference, use the resulting first power, and retain the original nonzero restriction even though the simplified expression alone would allow zero.
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