Question
Simplify the expression
224x3−21
Evaluate
7x2×32x−21
Solution
More Steps

Evaluate
7x2×32x
Multiply the terms
224x2×x
Multiply the terms with the same base by adding their exponents
224x2+1
Add the numbers
224x3
224x3−21
Show Solution

Factor the expression
7(32x3−3)
Evaluate
7x2×32x−21
Multiply
More Steps

Evaluate
7x2×32x
Multiply the terms
224x2×x
Multiply the terms with the same base by adding their exponents
224x2+1
Add the numbers
224x3
224x3−21
Solution
7(32x3−3)
Show Solution

Find the roots
x=436
Alternative Form
x≈0.45428
Evaluate
7x2×32x−21
To find the roots of the expression,set the expression equal to 0
7x2×32x−21=0
Multiply
More Steps

Multiply the terms
7x2×32x
Multiply the terms
224x2×x
Multiply the terms with the same base by adding their exponents
224x2+1
Add the numbers
224x3
224x3−21=0
Move the constant to the right-hand side and change its sign
224x3=0+21
Removing 0 doesn't change the value,so remove it from the expression
224x3=21
Divide both sides
224224x3=22421
Divide the numbers
x3=22421
Cancel out the common factor 7
x3=323
Take the 3-th root on both sides of the equation
3x3=3323
Calculate
x=3323
Simplify the root
More Steps

Evaluate
3323
To take a root of a fraction,take the root of the numerator and denominator separately
33233
Simplify the radical expression
More Steps

Evaluate
332
Write the expression as a product where the root of one of the factors can be evaluated
38×4
Write the number in exponential form with the base of 2
323×4
The root of a product is equal to the product of the roots of each factor
323×34
Reduce the index of the radical and exponent with 3
234
23433
Multiply by the Conjugate
234×34233×342
Simplify
234×34233×232
Multiply the numbers
More Steps

Evaluate
33×232
Multiply the terms
36×2
Use the commutative property to reorder the terms
236
234×342236
Multiply the numbers
More Steps

Evaluate
234×342
Multiply the terms
2×22
Calculate the product
23
23236
Reduce the fraction
More Steps

Evaluate
232
Use the product rule aman=an−m to simplify the expression
23−11
Subtract the terms
221
2236
x=2236
Solution
x=436
Alternative Form
x≈0.45428
Show Solution
