Algebra
Calculus
Trigonometry
Matrix
Question
Simplify the expression
115x385x
Evaluate
22x47x3×510x4
Simplify the root
More Steps
Evaluate
7x3
Rewrite the exponent as a sum
7x2+1
Use am+n=am×an to expand the expression
7x2×x
Reorder the terms
x2×7x
The root of a product is equal to the product of the roots of each factor
x2×7x
Reduce the index of the radical and exponent with 2
x7x
22x4x7x×510x4
Simplify the root
More Steps
Evaluate
10x4
Reorder the terms
x4×10
The root of a product is equal to the product of the roots of each factor
x4×10
Reduce the index of the radical and exponent with 2
10×x2
22x4x7x×510×x2
Simplify the root
More Steps
Evaluate
22x4
Reorder the terms
x4×22
The root of a product is equal to the product of the roots of each factor
x4×22
Reduce the index of the radical and exponent with 2
22×x2
22×x2x7x×510×x2
Multiply
More Steps
Evaluate
x7x×510×x2
Multiply the terms with the same base by adding their exponents
x1+27x×510
Add the numbers
x37x×510
22×x2x37x×510
Reduce the fraction
More Steps
Calculate
x2x3
Use the product rule aman=an−m to simplify the expression
x3−2
Subtract the terms
x1
Simplify
x
22x7x×510
Factor
22×1x7x×510
Factor the expression
22x7x×52×5
Factor the expression
2×11x7x×52×5
Reduce the fraction
11x7x×55
Simplify
More Steps
Evaluate
x7x×55
Use the commutative property to reorder the terms
5x7x×5
Use the commutative property to reorder the terms
5x35x
115x35x
Multiply by the Conjugate
11×115x35x×11
Calculate
115x35x×11
Solution
More Steps
Evaluate
35x×11
The product of roots with the same index is equal to the root of the product
35x×11
Calculate the product
385x
115x385x
Show Solution
Find the roots
x∈∅
Evaluate
22x47x3×510x4
To find the roots of the expression,set the expression equal to 0
22x47x3×510x4=0
Find the domain
More Steps
Evaluate
⎩⎨⎧7x3≥010x4≥022x4≥022x4=0
Calculate
More Steps
Evaluate
7x3≥0
Rewrite the expression
x3≥0
The only way a base raised to an odd power can be greater than or equal to 0 is if the base is greater than or equal to 0
x≥0
⎩⎨⎧x≥010x4≥022x4≥022x4=0
Since the left-hand side is always positive or 0,and the right-hand side is always 0,the statement is true for any value of x
⎩⎨⎧x≥0x∈R22x4≥022x4=0
Since the left-hand side is always positive or 0,and the right-hand side is always 0,the statement is true for any value of x
⎩⎨⎧x≥0x∈Rx∈R22x4=0
Calculate
More Steps
Evaluate
22x4=0
Calculate
22x4=0
Rewrite the expression
x4=0
The only way a power can not be 0 is when the base not equals 0
x=0
⎩⎨⎧x≥0x∈Rx∈Rx=0
Simplify
⎩⎨⎧x≥0x∈Rx=0
Find the intersection
x>0
22x47x3×510x4=0,x>0
Calculate
22x47x3×510x4=0
Simplify the root
More Steps
Evaluate
7x3
Rewrite the exponent as a sum
7x2+1
Use am+n=am×an to expand the expression
7x2×x
Reorder the terms
x2×7x
The root of a product is equal to the product of the roots of each factor
x2×7x
Reduce the index of the radical and exponent with 2
x7x
22x4x7x×510x4=0
Simplify the root
More Steps
Evaluate
10x4
Reorder the terms
x4×10
The root of a product is equal to the product of the roots of each factor
x4×10
Reduce the index of the radical and exponent with 2
10×x2
22x4x7x×510×x2=0
Simplify the root
More Steps
Evaluate
22x4
Reorder the terms
x4×22
The root of a product is equal to the product of the roots of each factor
x4×22
Reduce the index of the radical and exponent with 2
22×x2
22×x2x7x×510×x2=0
Multiply
More Steps
Multiply the terms
x7x×510×x2
Multiply the terms with the same base by adding their exponents
x1+27x×510
Add the numbers
x37x×510
Use the commutative property to reorder the terms
5x37x×10
Use the commutative property to reorder the terms
5x370x
22×x25x370x=0
Reduce the fraction
More Steps
Calculate
x2x3
Use the product rule aman=an−m to simplify the expression
x3−2
Subtract the terms
x1
Simplify
x
225x70x=0
Simplify
5x70x=0
Elimination the left coefficient
x70x=0
Separate the equation into 2 possible cases
x=070x=0
Solve the equation
More Steps
Evaluate
70x=0
The only way a root could be 0 is when the radicand equals 0
70x=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∈∅
Show Solution