Question
Simplify the expression
4x22x
Evaluate
x×x32x
Simplify the root
More Steps

Evaluate
32x
Rewrite the exponent as a sum
24+1x
Use am+n=am×an to expand the expression
24×2x
The root of a product is equal to the product of the roots of each factor
24×2x
Reduce the index of the radical and exponent with 2
42x
x×x×42x
Multiply the terms
x2×42x
Solution
4x22x
Show Solution

Find the roots
x=0
Evaluate
x×x32x
To find the roots of the expression,set the expression equal to 0
x×x32x=0
Find the domain
x×x32x=0,x≥0
Calculate
x×x32x=0
Simplify the root
More Steps

Evaluate
32x
Rewrite the exponent as a sum
24+1x
Use am+n=am×an to expand the expression
24×2x
The root of a product is equal to the product of the roots of each factor
24×2x
Reduce the index of the radical and exponent with 2
42x
x×x×42x=0
Multiply
More Steps

Multiply the terms
x×x×42x
Multiply the terms
x2×42x
Use the commutative property to reorder the terms
4x22x
4x22x=0
Elimination the left coefficient
x22x=0
Separate the equation into 2 possible cases
x2=02x=0
The only way a power can be 0 is when the base equals 0
x=02x=0
Solve the equation
More Steps

Evaluate
2x=0
The only way a root could be 0 is when the radicand equals 0
2x=0
Rewrite the expression
x=0
x=0x=0
Find the union
x=0
Check if the solution is in the defined range
x=0,x≥0
Solution
x=0
Show Solution
