Evaluate 243^(4/5)

Problem

243^(4/5)

Solution

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

243^(4/5)=(√(5,243))^4

2. Identify the fifth root of 243 by recognizing that 3^5=243

√(5,243)=3

3. Substitute the root back into the expression.

3^4

4. Calculate the final value by raising 3 to the fourth power.

3×3×3×3=81

Final Answer

243^(4/5)=81

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