Evaluate (1/64)^(2/3)

Problem

(1/64)2/3

Solution

1. Apply the power of a quotient rule by distributing the exponent to both the numerator and the denominator.

(1/64)2/3=1/64

2. Simplify the numerator because 1 raised to any power is 1.

1/64=1/64

3. Rewrite the denominator using the property am/n=(√(n,a))m to evaluate the cube root first.

1/64=1/((√(3,64))2)

4. Evaluate the cube root of 64, which is 4 because 4×4×4=64

1/((√(3,64))2)=1/4

5. Square the result to find the final value.

1/4=1/16

Final Answer

(1/64)2/3=1/16

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