Question
Simplify the expression
768x8−36864x7+774144x6−9289728x5+69672960x4−334430208x3+1003290624x2−6144×67x+768×68
Evaluate
48(x−6)5×16(x−6)3
Multiply the terms
768(x−6)5(x−6)3
Multiply the terms with the same base by adding their exponents
768(x−6)5+3
Add the numbers
768(x−6)8
Expand the expression
768(x8−48x7+1008x6−12096x5+90720x4−435456x3+1306368x2−67×8x+68)
Apply the distributive property
768x8−768×48x7+768×1008x6−768×12096x5+768×90720x4−768×435456x3+768×1306368x2−768×67×8x+768×68
Multiply the numbers
768x8−36864x7+768×1008x6−768×12096x5+768×90720x4−768×435456x3+768×1306368x2−768×67×8x+768×68
Multiply the numbers
768x8−36864x7+774144x6−768×12096x5+768×90720x4−768×435456x3+768×1306368x2−768×67×8x+768×68
Multiply the numbers
768x8−36864x7+774144x6−9289728x5+768×90720x4−768×435456x3+768×1306368x2−768×67×8x+768×68
Multiply the numbers
768x8−36864x7+774144x6−9289728x5+69672960x4−768×435456x3+768×1306368x2−768×67×8x+768×68
Multiply the numbers
768x8−36864x7+774144x6−9289728x5+69672960x4−334430208x3+768×1306368x2−768×67×8x+768×68
Multiply the numbers
768x8−36864x7+774144x6−9289728x5+69672960x4−334430208x3+1003290624x2−768×67×8x+768×68
Solution
768x8−36864x7+774144x6−9289728x5+69672960x4−334430208x3+1003290624x2−6144×67x+768×68
Show Solution

Find the roots
x=6
Evaluate
48(x−6)5×16(x−6)3
To find the roots of the expression,set the expression equal to 0
48(x−6)5×16(x−6)3=0
Multiply
More Steps

Multiply the terms
48(x−6)5×16(x−6)3
Multiply the terms
768(x−6)5(x−6)3
Multiply the terms with the same base by adding their exponents
768(x−6)5+3
Add the numbers
768(x−6)8
768(x−6)8=0
Rewrite the expression
(x−6)8=0
The only way a power can be 0 is when the base equals 0
x−6=0
Move the constant to the right-hand side and change its sign
x=0+6
Solution
x=6
Show Solution
