Question
Simplify the expression
8192x9−16384x8
Evaluate
(4x−8)(16x2×32x6×4)
Remove the parentheses
(4x−8)×16x2×32x6×4
Multiply the terms
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Evaluate
16×32×4
Multiply the terms
512×4
Multiply the numbers
2048
(4x−8)×2048x2×x6
Multiply the terms with the same base by adding their exponents
(4x−8)×2048x2+6
Add the numbers
(4x−8)×2048x8
Multiply the terms
2048x8(4x−8)
Apply the distributive property
2048x8×4x−2048x8×8
Multiply the terms
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Evaluate
2048x8×4x
Multiply the numbers
8192x8×x
Multiply the terms
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Evaluate
x8×x
Use the product rule an×am=an+m to simplify the expression
x8+1
Add the numbers
x9
8192x9
8192x9−2048x8×8
Solution
8192x9−16384x8
Show Solution

Factor the expression
8192x8(x−2)
Evaluate
(4x−8)(16x2×32x6×4)
Remove the parentheses
(4x−8)×16x2×32x6×4
Multiply
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Multiply the terms
16x2×32x6×4
Multiply the terms
More Steps

Evaluate
16×32×4
Multiply the terms
512×4
Multiply the numbers
2048
2048x2×x6
Multiply the terms with the same base by adding their exponents
2048x2+6
Add the numbers
2048x8
(4x−8)×2048x8
Multiply the terms
2048x8(4x−8)
Factor the expression
2048x8×4(x−2)
Solution
8192x8(x−2)
Show Solution

Find the roots
x1=0,x2=2
Evaluate
(4x−8)(16x2×32x6×4)
To find the roots of the expression,set the expression equal to 0
(4x−8)(16x2×32x6×4)=0
Multiply
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Multiply the terms
16x2×32x6×4
Multiply the terms
More Steps

Evaluate
16×32×4
Multiply the terms
512×4
Multiply the numbers
2048
2048x2×x6
Multiply the terms with the same base by adding their exponents
2048x2+6
Add the numbers
2048x8
(4x−8)×2048x8=0
Multiply the terms
2048x8(4x−8)=0
Elimination the left coefficient
x8(4x−8)=0
Separate the equation into 2 possible cases
x8=04x−8=0
The only way a power can be 0 is when the base equals 0
x=04x−8=0
Solve the equation
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Evaluate
4x−8=0
Move the constant to the right-hand side and change its sign
4x=0+8
Removing 0 doesn't change the value,so remove it from the expression
4x=8
Divide both sides
44x=48
Divide the numbers
x=48
Divide the numbers
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Evaluate
48
Reduce the numbers
12
Calculate
2
x=2
x=0x=2
Solution
x1=0,x2=2
Show Solution
