Question
Solve the system of equations
Solution
a=0
Evaluate
{6a6=2(a×16)×6a62(a×16)×6a6=2(a×16)
Remove the parentheses
{6a6=2a×16×6a62a×16×6a6=2a×16
Calculate
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Evaluate
6a6=2a×16×6a6
Multiply
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Evaluate
2a×16×6a6
Multiply the terms
192a×a6
Multiply the terms with the same base by adding their exponents
192a1+6
Add the numbers
192a7
6a6=192a7
Add or subtract both sides
6a6−192a7=0
Factor the expression
6a6(1−32a)=0
Divide both sides
a6(1−32a)=0
Separate the equation into 2 possible cases
a6=0∪1−32a=0
The only way a power can be 0 is when the base equals 0
a=0∪1−32a=0
Solve the equation
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Evaluate
1−32a=0
Move the constant to the right-hand side and change its sign
−32a=0−1
Removing 0 doesn't change the value,so remove it from the expression
−32a=−1
Change the signs on both sides of the equation
32a=1
Divide both sides
3232a=321
Divide the numbers
a=321
a=0∪a=321
{a=0∪a=3212a×16×6a6=2a×16
Calculate
{a=0∪a=321a×16×6a6=a×16
Calculate
{a=0∪a=321a×6a6=a
Calculate
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Evaluate
a×6a6=a
Multiply
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Evaluate
a×6a6
Multiply the terms with the same base by adding their exponents
a1+6×6
Add the numbers
a7×6
Use the commutative property to reorder the terms
6a7
6a7=a
Add or subtract both sides
6a7−a=0
Factor the expression
a(6a6−1)=0
Separate the equation into 2 possible cases
a=0∪6a6−1=0
Solve the equation
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Evaluate
6a6−1=0
Move the constant to the right-hand side and change its sign
6a6=0+1
Removing 0 doesn't change the value,so remove it from the expression
6a6=1
Divide both sides
66a6=61
Divide the numbers
a6=61
Take the root of both sides of the equation and remember to use both positive and negative roots
a=±661
Simplify the expression
a=±667776
Separate the equation into 2 possible cases
a=667776∪a=−667776
a=0∪a=667776∪a=−667776
{a=0∪a=321a=0∪a=667776∪a=−667776
Find the intersection
a=0
Solution
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Check the solution
{6(06)=2(0×16)×6(06)2(0×16)×6(06)=2(0×16)
Simplify
{0=00=0
Evaluate
true
a=0
Show Solution