Evaluate 16^(-3/2)

Problem

16(−3/2)

Solution

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

16(−3/2)=1/(16(3/2))

2. Interpret the rational exponent using the rule a(m/n)=(√(n,a))m where the denominator 2 represents a square root.

1/(16(3/2))=1/((√(,16))3)

3. Evaluate the square root of the base number.

√(,16)=4

4. Substitute the result back into the expression.

1/4

5. Calculate the power by multiplying the base by itself the specified number of times.

4=4×4×4=64

Final Answer

16(−3/2)=1/64

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