Evaluate 32^(4/5)

Problem

32^(4/5)

Solution

1. Rewrite the expression using the property of rational exponents a^(m/n)=(√(n,a))^m

32^(4/5)=(√(5,32))^4

2. Evaluate the fifth root of 32 by identifying that 2^5=32

√(5,32)=2

3. Substitute the root back into the expression.

2^4

4. Calculate the final value by raising 2 to the power of 4

2⋅2⋅2⋅2=16

Final Answer

32^(4/5)=16

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