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 2^4=16

√(4,16)=2

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

1/2^3=1/8

Final Answer

16^(−3/4)=1/8

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