Simplify square root of x^9

Problem

√(,x^9)

Solution

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

√(,x^9)=(x^9)^1/2

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

(x^9)^1/2=x^9/2

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

x^9/2=x^(4+1/2)

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

x^4⋅x^1/2

5. Convert the fractional exponent back into radical notation.

x^4√(,x)

Final Answer

√(,x^9)=x^4√(,x)

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