Evaluate 64^(-2/3)

Problem

64(−2/3)

Solution

1. Apply the negative exponent rule by rewriting the expression as the reciprocal with a positive exponent.

64(−2/3)=1/(64(2/3))

2. Rewrite the rational exponent using the property a(m/n)=(√(n,a))m

1/(64(2/3))=1/((√(3,64))2)

3. Evaluate the cube root of 64, which is the number that, when multiplied by itself three times, equals 64.

√(3,64)=4

4. Substitute the root back into the expression and square the result.

1/4=1/16

Final Answer

64(−2/3)=1/16

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