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 4^4=256

√(4,256)=4

4. Substitute the root back into the expression.

1/4^3

5. Calculate the power of the denominator.

4^3=64

Final Answer

256^(−3/4)=1/64

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