Simplify (u^(1/4))/(u^(1/6))

Problem

(u^(1/4))/(u^(1/6))

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^(1/4−1/6)

3. Find a common denominator for the fractions in the exponent, which is 12

1/4=3/12

1/6=2/12

4. Perform the subtraction in the exponent.

3/12−2/12=1/12

5. Rewrite the expression with the new exponent.

u^(1/12)

Final Answer

(u^(1/4))/(u^(1/6))=u^(1/12)

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