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

Problem

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

Solution

1. Identify the rule for dividing powers with the same base, which states that (a^m)/(a^n)=a^(m−n)

2. Subtract the exponent in the denominator from the exponent in the numerator.

u^(3/2−1/3)

3. Find a common denominator for the fractions in the exponent, which is 6

3/2=9/6

1/3=2/6

4. Perform the subtraction of the fractions.

9/6−2/6=7/6

5. Rewrite the expression with the new exponent.

u^(7/6)

Final Answer

(u^(3/2))/(u^(1/3))=u^(7/6)

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