Simplify ( cube root of y)^2

Problem

(√(3,y))2

Solution

1. Rewrite the radical expression using a fractional exponent. The cube root of y is equivalent to y raised to the power of 1/3

(√(3,y))2=(y1/3)2

2. Apply the power of a power rule, which states that (am)n=a(m⋅n) Multiply the exponents 1/3 and 2

1/3⋅2=2/3

3. Simplify the expression by writing the result with the new exponent.

y2/3

4. Convert back to radical notation if desired. The denominator of the exponent becomes the index of the root, and the numerator becomes the power.

√(3,y2)

Final Answer

(√(3,y))2=√(3,y2)

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