Evaluate 64^(-4/3)

Problem

64^(−4/3)

Solution

1. Rewrite the expression using the property of negative exponents, a^(−n)=1/(a^n)

1/(64^(4/3))

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

1/((√(3,64))^4)

3. Evaluate the cube root of 64, noting that 4^3=64

1/4^4

4. Calculate the value of 4 raised to the power of 4.

1/256

Final Answer

64^(−4/3)=1/256

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