Simplify cube root of x^7

Problem

√(3,x7)

Solution

1. Rewrite the radical expression using a fractional exponent to make it easier to manipulate.

√(3,x7)=x(7/3)

2. Decompose the fraction into a whole number and a proper fraction by dividing the exponent.

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

3. Apply the product rule for exponents to separate the whole number power from the fractional power.

x(2+1/3)=x2⋅x(1/3)

4. Convert the fractional power back into radical form to reach the final simplified expression.

x2⋅x(1/3)=x2√(3,x)

Final Answer

√(3,x7)=x2√(3,x)

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