Question
Simplify the expression
271x12
Evaluate
(3x−2×x−1x−3)−3
Dividing by an is the same as multiplying by a−n
(3x−2×x−3×x)−3
Multiply
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Multiply the terms
3x−2×x−3×x
Multiply the terms with the same base by adding their exponents
3x−2−3+1
Calculate the sum or difference
3x−4
(3x−4)−3
To raise a product to a power,raise each factor to that power
3−3(x−4)−3
Evaluate the power
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Evaluate
3−3
Rewrite the expression
331
Simplify
271
271(x−4)−3
Solution
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Evaluate
(x−4)−3
Multiply the exponents
x−4(−3)
Multiply the terms
x12
271x12
Show Solution

Find the roots
x∈/R
Evaluate
(3x−2×x−1x−3)−3
To find the roots of the expression,set the expression equal to 0
(3x−2×x−1x−3)−3=0
Find the domain
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Evaluate
⎩⎨⎧x=0x−1=03x−2×x−1x−3=0
Calculate
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Evaluate
x−1=0
Rearrange the terms
x1=0
Calculate
{1=0x=0
The statement is true for any value of x
{x∈Rx=0
Find the intersection
x=0
⎩⎨⎧x=0x=03x−2×x−1x−3=0
Calculate
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Evaluate
3x−2×x−1x−3=0
Simplify
3x−4=0
Rewrite the expression
x−4=0
Rearrange the terms
x41=0
Calculate
{1=0x4=0
The statement is true for any value of x
{x∈Rx4=0
The only way a power can not be 0 is when the base not equals 0
{x∈Rx=0
Find the intersection
x=0
⎩⎨⎧x=0x=0x=0
Simplify
x=0
(3x−2×x−1x−3)−3=0,x=0
Calculate
(3x−2×x−1x−3)−3=0
Divide the terms
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Evaluate
x−1x−3
Use the product rule aman=an−m to simplify the expression
x−1−(−3)1
Reduce the fraction
x21
(3x−2×x21)−3=0
Multiply the terms
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Multiply the terms
3x−2×x21
Rewrite the expression
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Evaluate
3x−2
Express with a positive exponent using a−n=an1
3×x21
Rewrite the expression
x23
x23×x21
Multiply the terms
x2×x23
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
x43
(x43)−3=0
Solution
x∈/R
Show Solution
