Evaluate (3/4)^3

Problem

(3/4)3

Solution

1. Apply the power of a quotient rule, which states that for any fraction raised to a power, you raise both the numerator and the denominator to that power.

(a/b)n=(an)/(bn)

2. Substitute the values from the expression into the rule.

(3/4)3=3/4

3. Calculate the numerator by multiplying 3 by itself three times.

3=3⋅3⋅3=27

4. Calculate the denominator by multiplying 4 by itself three times.

4=4⋅4⋅4=64

5. Combine the results into a single fraction.

27/64

Final Answer

(3/4)3=27/64

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