Simplify square root of x^9

Problem

√(,x9)

Solution

1. Rewrite the expression using a fractional exponent to represent the square root.

√(,x9)=(x9)1/2

2. Apply the power of a power rule, which states that (am)n=a(m⋅n)

(x9)1/2=x9/2

3. Decompose the exponent into an integer part and a fractional part to simplify the radical.

x9/2=x(4+1/2)

4. Separate the terms using the product rule for exponents, a(m+n)=am⋅an

x4⋅x1/2

5. Convert the fractional exponent back into radical notation.

x4√(,x)

Final Answer

√(,x9)=x4√(,x)

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