Simplify cube root of y^7

Problem

√(3,y7)

Solution

1. Rewrite the radical using a fractional exponent to make the simplification clearer.

√(3,y7)=y(7/3)

2. Decompose the fraction into an integer and a proper fraction by dividing the exponent by the index.

y(7/3)=y(2+1/3)

3. Apply the product rule for exponents to separate the terms.

y(2+1/3)=y2⋅y(1/3)

4. Convert the term with the fractional exponent back into radical form.

y2⋅y(1/3)=y2√(3,y)

Final Answer

√(3,y7)=y2√(3,y)

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