Evaluate 4^(-3/2)

Problem

4(−3/2)

Solution

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

4(−3/2)=1/(4(3/2))

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

1/(4(3/2))=1/((√(,4))3)

3. Evaluate the square root of the base.

1/((√(,4))3)=1/2

4. Calculate the power in the denominator.

1/2=1/8

Final Answer

4(−3/2)=1/8

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