Simplify square root of x^3

Problem

√(,x3)

Solution

1. Identify the expression as a square root of a power, which can be written using a fractional exponent.

√(,x3)=(x3)1/2

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

(x3)1/2=x(3⋅1/2)

3. Multiply the exponents to find the simplified power.

x(3⋅1/2)=x3/2

4. Rewrite the expression in radical form by separating the exponent into a whole number and a fraction, assuming x≥0

x3/2=x1⋅x1/2

5. Simplify the result by converting the fractional exponent back into a radical.

x1⋅x1/2=x√(,x)

Final Answer

√(,x3)=x√(,x)

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