Question
Simplify the expression
1125x614
Evaluate
3x2×15x4×x2×10x2×57x
Reduce the fraction
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Evaluate
x2×10x2×57x
Multiply
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Evaluate
x2×10x2×5
Multiply the terms with the same base by adding their exponents
x2+2×10×5
Add the numbers
x4×10×5
Multiply the terms
x4×50
x4×507x
Reduce the fraction
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Calculate
x4x
Use the product rule aman=an−m to simplify the expression
x4−11
Subtract the terms
x31
x3×507
Calculate
50x37
3x2×15x4×50x37
Multiply
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Multiply the terms
3x2×15x
Multiply the terms
45x2×x
Multiply the terms with the same base by adding their exponents
45x2+1
Add the numbers
45x3
45x34×50x37
Cancel out the common factor 2
45x32×25x37
Multiply the terms
45x3×25x32×7
Multiply the terms
45x3×25x314
Solution
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Evaluate
45x3×25x3
Multiply the numbers
1125x3×x3
Multiply the terms
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Evaluate
x3×x3
Use the product rule an×am=an+m to simplify the expression
x3+3
Add the numbers
x6
1125x6
1125x614
Show Solution

Find the excluded values
x=0
Evaluate
3x2×15x4×x2×10x2×57x
To find the excluded values,set the denominators equal to 0
x2×x=0x2×x2=0
Solve the equations
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Evaluate
x2×x=0
Multiply the terms
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Evaluate
x2×x
Use the product rule an×am=an+m to simplify the expression
x2+1
Add the numbers
x3
x3=0
The only way a power can be 0 is when the base equals 0
x=0
x=0x2×x2=0
Solve the equations
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Evaluate
x2×x2=0
Multiply the terms
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Evaluate
x2×x2
Use the product rule an×am=an+m to simplify the expression
x2+2
Add the numbers
x4
x4=0
The only way a power can be 0 is when the base equals 0
x=0
x=0x=0
Solution
x=0
Show Solution

Find the roots
x∈∅
Evaluate
3x2×15x4×x2×10x2×57x
To find the roots of the expression,set the expression equal to 0
3x2×15x4×x2×10x2×57x=0
Find the domain
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Evaluate
{x2×x=0x2×x2=0
Calculate
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Evaluate
x2×x=0
Multiply the terms
x3=0
The only way a power can not be 0 is when the base not equals 0
x=0
{x=0x2×x2=0
Calculate
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Evaluate
x2×x2=0
Multiply the terms
x4=0
The only way a power can not be 0 is when the base not equals 0
x=0
{x=0x=0
Find the intersection
x=0
3x2×15x4×x2×10x2×57x=0,x=0
Calculate
3x2×15x4×x2×10x2×57x=0
Multiply
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Multiply the terms
3x2×15x
Multiply the terms
45x2×x
Multiply the terms with the same base by adding their exponents
45x2+1
Add the numbers
45x3
45x34×x2×10x2×57x=0
Multiply
More Steps

Multiply the terms
x2×10x2×5
Multiply the terms with the same base by adding their exponents
x2+2×10×5
Add the numbers
x4×10×5
Multiply the terms
x4×50
Use the commutative property to reorder the terms
50x4
45x34×50x47x=0
Divide the terms
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Evaluate
50x47x
Use the product rule aman=an−m to simplify the expression
50x4−17
Reduce the fraction
50x37
45x34×50x37=0
Multiply the terms
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Multiply the terms
45x34×50x37
Cancel out the common factor 2
45x32×25x37
Multiply the terms
45x3×25x32×7
Multiply the terms
45x3×25x314
Multiply the terms
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Evaluate
45x3×25x3
Multiply the numbers
1125x3×x3
Multiply the terms
1125x6
1125x614
1125x614=0
Cross multiply
14=1125x6×0
Simplify the equation
14=0
Solution
x∈∅
Show Solution
