Evaluate (4/3)^-3

Problem

(4/3)^(−3)

Solution

1. Apply the negative exponent rule, which states that a^(−n)=1/(a^n) or (a/b)^(−n)=(b/a)^n

(4/3)^(−3)=(3/4)^3

2. Apply the power of a quotient rule, which states that (a/b)^n=(a^n)/(b^n)

(3/4)^3=3^3/4^3

3. Evaluate the powers in the numerator and the denominator.

3^3=27

4^3=64

4. Combine the results into a single fraction.

27/64

Final Answer

(4/3)^(−3)=27/64

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