Evaluate 27^(-4/3)

Problem

27^(−4/3)

Solution

1. Rewrite the negative exponent as a reciprocal using the rule a^(−n)=1/(a^n)

27^(−4/3)=1/(27^(4/3))

2. Apply the rational exponent rule a^(m/n)=(√(n,a))^m to the denominator.

1/(27^(4/3))=1/((√(3,27))^4)

3. Evaluate the cube root of 27, noting that 3^3=27

√(3,27)=3

4. Substitute the result back into the expression.

1/3^4

5. Calculate the power of 3 in the denominator.

3^4=81

Final Answer

27^(−4/3)=1/81

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