Simplify u^(3/2)u^(1/3)

Problem

u(3/2)*u(1/3)

Solution

1. Identify the operation as the multiplication of two exponential expressions with the same base u

2. Apply the product rule for exponents, which states that am*an=a(m+n)

3. Add the exponents by finding a common denominator for 3/2 and 1/3

4. Find the common denominator, which is 6

5. Convert the fractions to have the denominator 6 3/2=9/6 and 1/3=2/6

6. Sum the numerators to get the final exponent: 9/6+2/6=11/6

Final Answer

u(3/2)*u(1/3)=u(11/6)

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