Evaluate 125^(-4/3)

Problem

125^(−4/3)

Solution

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

1/(125^(4/3))

2. Apply the definition of rational exponents a^(m/n)=(√(n,a))^m to the denominator.

1/((√(3,125))^4)

3. Evaluate the cube root of 125 noting that 5^3=125

1/5^4

4. Calculate the fourth power of 5 which is 5×5×5×5=625

1/625

Final Answer

125^(−4/3)=1/625

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