Simplify cube root of 125x^9

Problem

√(3,125*x9)

Solution

1. Rewrite the expression using the property of radicals that allows the cube root to be distributed across factors: √(3,a⋅b)=√(3,a)⋅√(3,b)

√(3,125)⋅√(3,x9)

2. Evaluate the cube root of the numerical coefficient by identifying that 5=125

√(3,125)=5

3. Simplify the variable part by applying the rule for radicals and exponents, √(n,xm)=x(m/n)

√(3,x9)=x(9/3)

4. Divide the exponent to find the final power of x

x(9/3)=x3

5. Combine the simplified numerical and variable parts.

5⋅x3

Final Answer

√(3,125*x9)=5*x3

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