Evaluate (-1024)^(1/5)

Problem

(−1024)(1/5)

Solution

1. Identify the operation as finding the fifth root of a negative number.

2. Rewrite the base number as a power of a smaller integer.

1024=2

3. Apply the power of a power property to express the base as a fifth power.

1024=(2)5

1024=4

4. Substitute the power back into the original expression, noting that for odd roots, the negative sign can be moved outside or associated with the base.

(−1024)(1/5)=((−4)5)(1/5)

5. Simplify by multiplying the exponents.

5⋅1/5=1

(−4)1=−4

Final Answer

(−1024)(1/5)=−4

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