Evaluate 16^(5/4)

Problem

16(5/4)

Solution

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

16(5/4)=(√(4,16))5

2. Evaluate the fourth root of 16 by finding the number that, when multiplied by itself four times, equals 16.

√(4,16)=2

3. Substitute the root back into the expression.

2

4. Calculate the final value by raising 2 to the power of 5.

2×2×2×2×2=32

Final Answer

16(5/4)=32

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