Question
Simplify the expression
72x2x
Evaluate
32(9x)3×4x
Simplify the root
More Steps

Evaluate
9x
Rewrite the exponent as a sum
32x
The root of a product is equal to the product of the roots of each factor
32×x
Reduce the index of the radical and exponent with 2
3x
32(3x)3×4x
Multiply the terms
More Steps

Evaluate
32×4
Multiply the numbers
32×4
Multiply the numbers
38
38(3x)3x
Multiply the terms
More Steps

Evaluate
38(3x)3
Rewrite the expression
38×33(x)3
Reduce the fraction
8×32xx
Rewrite the expression
8×9xx
Multiply the terms
72xx
72xx×x
Solution
72x2x
Show Solution

Find the roots
x=0
Evaluate
32(9x)3×4x
To find the roots of the expression,set the expression equal to 0
32(9x)3×4x=0
Find the domain
32(9x)3×4x=0,x≥0
Calculate
32(9x)3×4x=0
Simplify the root
More Steps

Evaluate
9x
Rewrite the exponent as a sum
32x
The root of a product is equal to the product of the roots of each factor
32×x
Reduce the index of the radical and exponent with 2
3x
32(3x)3×4x=0
Multiply
More Steps

Multiply the terms
32(3x)3×4x
Multiply the terms
More Steps

Evaluate
32×4
Multiply the numbers
32×4
Multiply the numbers
38
38(3x)3x
Multiply the terms
More Steps

Evaluate
38(3x)3
Rewrite the expression
38×33(x)3
Reduce the fraction
8×32xx
Rewrite the expression
8×9xx
Multiply the terms
72xx
72xx×x
Multiply the terms
72x2x
72x2x=0
Elimination the left coefficient
x2x=0
Separate the equation into 2 possible cases
x2=0x=0
The only way a power can be 0 is when the base equals 0
x=0x=0
The only way a root could be 0 is when the radicand equals 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
