Evaluate 4^(-5/2)

Problem

4^(−5/2)

Solution

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

4^(−5/2)=1/(4^(5/2))

2. Apply the rational exponent rule which states that a^(m/n)=(√(n,a))^m

1/(4^(5/2))=1/((√(,4))^5)

3. Evaluate the square root of the base number.

√(,4)=2

4. Substitute the root back into the expression.

1/2^5

5. Calculate the power of the denominator.

2^5=32

Final Answer

4^(−5/2)=1/32

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