Evaluate 27^(-4/3)

Problem

27(−4/3)

Solution

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

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=27

√(3,27)=3

4. Substitute the result back into the expression.

1/3

5. Calculate the power of 3 in the denominator.

3=81

Final Answer

27(−4/3)=1/81

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