Evaluate 16^(-3/4)

Problem

16(−3/4)

Solution

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

16(−3/4)=1/(16(3/4))

2. Rewrite the rational exponent using the property a(m/n)=(√(n,a))m to separate the root and the power.

1/(16(3/4))=1/((√(4,16))3)

3. Evaluate the fourth root of the base number, noting that 2=16

√(4,16)=2

4. Substitute the root back into the expression and calculate the power.

1/2=1/8

Final Answer

16(−3/4)=1/8

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