Question
Simplify the expression
8n3−486
Evaluate
n2×8n−486
Solution
More Steps

Evaluate
n2×8n
Multiply the terms with the same base by adding their exponents
n2+1×8
Add the numbers
n3×8
Use the commutative property to reorder the terms
8n3
8n3−486
Show Solution

Factor the expression
2(4n3−243)
Evaluate
n2×8n−486
Multiply
More Steps

Evaluate
n2×8n
Multiply the terms with the same base by adding their exponents
n2+1×8
Add the numbers
n3×8
Use the commutative property to reorder the terms
8n3
8n3−486
Solution
2(4n3−243)
Show Solution

Find the roots
n=23318
Alternative Form
n≈3.931112
Evaluate
n2×8n−486
To find the roots of the expression,set the expression equal to 0
n2×8n−486=0
Multiply
More Steps

Multiply the terms
n2×8n
Multiply the terms with the same base by adding their exponents
n2+1×8
Add the numbers
n3×8
Use the commutative property to reorder the terms
8n3
8n3−486=0
Move the constant to the right-hand side and change its sign
8n3=0+486
Removing 0 doesn't change the value,so remove it from the expression
8n3=486
Divide both sides
88n3=8486
Divide the numbers
n3=8486
Cancel out the common factor 2
n3=4243
Take the 3-th root on both sides of the equation
3n3=34243
Calculate
n=34243
Solution
More Steps

Evaluate
34243
To take a root of a fraction,take the root of the numerator and denominator separately
343243
Simplify the radical expression
More Steps

Evaluate
3243
Write the expression as a product where the root of one of the factors can be evaluated
327×9
Write the number in exponential form with the base of 3
333×9
The root of a product is equal to the product of the roots of each factor
333×39
Reduce the index of the radical and exponent with 3
339
34339
Multiply by the Conjugate
34×342339×342
Simplify
34×342339×232
Multiply the numbers
More Steps

Evaluate
339×232
Multiply the terms
639×32
Multiply the terms
6318
34×3426318
Multiply the numbers
More Steps

Evaluate
34×342
The product of roots with the same index is equal to the root of the product
34×42
Calculate the product
343
Transform the expression
326
Reduce the index of the radical and exponent with 3
22
226318
Rewrite the expression
222×3318
Reduce the fraction
More Steps

Evaluate
222
Use the product rule aman=an−m to simplify the expression
22−11
Subtract the terms
211
Simplify
21
23318
n=23318
Alternative Form
n≈3.931112
Show Solution
