Question
Simplify the expression
−6480iJ3a3n2Y2o2u21
Evaluate
84Jian×2You×16Jia×3You×33Jian×1×You×54You×2
Reduce the fraction
84Jian×2You×16Jia×3You×33Jian×1×ou×54ou×2
Reduce the fraction
84Jian×2You×16Jia×3You×33Jian×1×u×54u×2
Reduce the fraction
84Jian×2You×16Jia×3You×33Jian×1×54×2
Multiply the numbers
84Jian×2You×16Jia×3You×33Jian×1×58
Multiply the terms
More Steps

Multiply the terms
3Jian×1×5
Rewrite the expression
3Jian×5
Multiply the terms
15Jian
Multiply the numbers
15iJan
84Jian×2You×16Jia×3You×315iJan8
Divide the terms
More Steps

Evaluate
15iJan8
Calculate
More Steps

Evaluate
15i8
Multiply by the Conjugate
15i×i8i
Calculate
−158i
Use b−a=−ba=−ba to rewrite the fraction
−158i
Reduce the fraction
−158i
Jan−158i
Use b−a=−ba=−ba to rewrite the fraction
−Jan158i
84Jian×2You×16Jia×3You×3−Jan158i
Multiply
More Steps

Multiply the terms
6Jia×3You×3
Multiply the terms
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Evaluate
6×3×3
Multiply the terms
18×3
Multiply the numbers
54
54JiaYou
Multiply the numbers
54iJaYou
84Jian×2You×154iJaYou−Jan158i
Divide the terms
More Steps

Evaluate
54iJaYou−Jan158i
Multiply by the reciprocal
−Jan158i×54iJaYou1
Rewrite the expression
−Jani×158×54iJaYou1
Rewrite the expression
−Jani×158×i×54JaYou1
Cancel out the common factor i
−Jan158×54JaYou1
Multiply the terms
−Jan×54JaYou158
Multiply the terms
More Steps

Evaluate
Jan×54JaYou
Use the commutative property to reorder the terms
54JanJaYou
Multiply the terms
54J2anaYou
Multiply the terms
54J2a2nYou
−54J2a2nYou158
Simplify
−810J2a2nYou8
84Jian×2You×1−810J2a2nYou8
Multiply the terms
More Steps

Multiply the terms
4Jian×2You×1
Rewrite the expression
4Jian×2You
Multiply the terms
8JianYou
Multiply the numbers
8iJanYou
88iJanYou−810J2a2nYou8
Divide the terms
More Steps

Evaluate
8iJanYou−810J2a2nYou8
Multiply by the reciprocal
−810J2a2nYou8×8iJanYou1
Cancel out the common factor 8
−810J2a2nYou1×iJanYou1
Multiply the terms
−810J2a2nYouiJanYou1
Multiply the terms
More Steps

Evaluate
810J2a2nYouiJanYou
Multiply the numbers
810iJ2a2nYouJanYou
Multiply the terms
810iJ3a2nYouanYou
Multiply the terms
810iJ3a3nYounYou
Multiply the terms
810iJ3a3n2YouYou
Multiply the terms
810iJ3a3n2Y2ouou
Multiply the terms
810iJ3a3n2Y2o2u×u
Multiply the terms
810iJ3a3n2Y2o2u2
−810iJ3a3n2Y2o2u21
8−810iJ3a3n2Y2o2u21
Multiply by the reciprocal
−810iJ3a3n2Y2o2u21×81
Multiply the terms
−810iJ3a3n2Y2o2u2×81
Solution
−6480iJ3a3n2Y2o2u21
Show Solution

Find the excluded values
J=0,a=0,n=0,Y=0,o=0,u=0
Evaluate
84Jian×2You×16Jia×3You×33Jian×1×You×54You×2
To find the excluded values,set the denominators equal to 0
JanYou=0JaYou=0
Solve the equations
More Steps

Evaluate
JanYou=0
Separate the equation into 6 possible cases
J=0a=0n=0Y=0o=0u=0
Find the union
J=0Y=0a=0n=0o=0u=0
J=0a=0n=0Y=0o=0u=0JaYou=0
Solve the equations
More Steps

Evaluate
JaYou=0
Separate the equation into 5 possible cases
J=0a=0Y=0o=0u=0
Find the union
J=0Y=0a=0o=0u=0
J=0a=0n=0Y=0o=0u=0J=0a=0Y=0o=0u=0
Solution
J=0,a=0,n=0,Y=0,o=0,u=0
Show Solution
