Evaluate 64^(5/6)

Problem

64(5/6)

Solution

1. Rewrite the base 64 as a power of 2 to simplify the expression.

64=2

2. Substitute the power into the original expression.

(2)(5/6)

3. Apply the power of a power rule, which states (am)n=a(m⋅n)

2(6⋅5/6)

4. Simplify the exponent by multiplying the terms.

6⋅5/6=5

5. Evaluate the resulting exponential expression.

2=32

Final Answer

64(5/6)=32

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