Evaluate (3/4)^-3

Problem

(3/4)(−3)

Solution

1. Apply the negative exponent rule, which states that a(−n)=1/(an) For a fraction, this means taking the reciprocal of the base and changing the sign of the exponent.

(3/4)(−3)=(4/3)3

2. Distribute the exponent to both the numerator and the denominator using the power of a quotient rule.

(4/3)3=4/3

3. Calculate the powers by multiplying the numbers.

4=64

3=27

4. Combine the results into a single fraction.

64/27

Final Answer

(3/4)(−3)=64/27

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