Evaluate 64^(-1/3)

Problem

64(−1/3)

Solution

1. Apply the negative exponent rule which states that a(−n)=1/(an)

1/(64(1/3))

2. Rewrite the fractional exponent as a radical using the rule a(1/n)=√(n,a)

1/√(3,64)

3. Evaluate the cube root by finding the number that, when multiplied by itself three times, equals 64 Since 4×4×4=64 the cube root is 4

1/4

Final Answer

64(−1/3)=1/4

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