Evaluate (1/3)^-3

Problem

(1/3)^(−3)

Solution

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

2. Apply the rule by taking the reciprocal of the base 1/3 and changing the sign of the exponent from −3 to 3

(1/3)^(−3)=(3/1)^3

3. Simplify the base inside the parentheses.

(3/1)^3=3^3

4. Calculate the value of the base raised to the power of 3.

3×3×3=27

Final Answer

(1/3)^(−3)=27

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