Evaluate 256^(-3/4)

Problem

256(−3/4)

Solution

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

256(−3/4)=1/(256(3/4))

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

1/(256(3/4))=1/((√(4,256))3)

3. Evaluate the fourth root of 256 by identifying that 4=256

√(4,256)=4

4. Substitute the root back into the expression.

1/4

5. Calculate the power of the denominator.

4=64

Final Answer

256(−3/4)=1/64

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