Evaluate (8/27)^(2/3)

Problem

(8/27)^(2/3)

Solution

1. Apply the power of a quotient rule to distribute the exponent to both the numerator and the denominator.

(8/27)^(2/3)=(8^(2/3))/(27^(2/3))

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

(8^(2/3))/(27^(2/3))=((√(3,8))^2)/((√(3,27))^2)

3. Evaluate the cube roots in the numerator and denominator.

√(3,8)=2

√(3,27)=3

4. Substitute the roots back into the expression and square the results.

2^2/3^2=4/9

Final Answer

(8/27)^(2/3)=4/9

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