Question
Simplify the expression
2xx
Evaluate
(16x2)−41
To raise a product to a power,raise each factor to that power
16−41(x2)−41
Evaluate the power
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Evaluate
16−41
Rewrite the expression
16411
Simplify
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Evaluate
1641
Rewrite in exponential form
(24)41
Multiply the exponents
24×41
Multiply the exponents
2
21
21(x2)−41
Evaluate the power
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Evaluate
(x2)−41
Multiply the exponents
x2(−41)
Multiply the terms
x−21
21x−21
Express with a positive exponent using a−n=an1
21×x211
Rewrite the expression
2x211
Use anm=nam to transform the expression
2x1
Multiply by the Conjugate
2x×x1×x
Calculate
2x1×x
Solution
2xx
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Find the roots
x∈∅
Evaluate
(16x2)−41
To find the roots of the expression,set the expression equal to 0
(16x2)−41=0
Find the domain
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Evaluate
{16x2>016x2=0
Calculate
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Evaluate
16x2>0
Since the left-hand side is always positive or 0,and the right-hand side is always 0,the statement is true for any value of x,except when 16x2=0
16x2=0
Rewrite the expression
x2=0
The only way a power can be 0 is when the base equals 0
x=0
Exclude the impossible values of x
x=0
{x=016x2=0
Calculate
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Evaluate
16x2=0
Rewrite the expression
x2=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
(16x2)−41=0,x=0
Calculate
(16x2)−41=0
Rewrite the expression
(16x2)411=0
Cross multiply
1=(16x2)41×0
Simplify the equation
1=0
Solution
x∈∅
Show Solution
