Question
Simplify the expression
x3x2x−913x7
Evaluate
3x23−9x261×x−21
Multiply
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Evaluate
9x261×x−21
Multiply the terms with the same base by adding their exponents
9x261−21
Subtract the numbers
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Evaluate
261−21
Reduce fractions to a common denominator
261−2×1313
Multiply the numbers
261−2613
Write all numerators above the common denominator
261−13
Subtract the numbers
26−12
Cancel out the common factor 2
13−6
Use b−a=−ba=−ba to rewrite the fraction
−136
9x−136
3x23−9x−136
Rewrite the expression
More Steps

Evaluate
−9x−136
Express with a positive exponent using a−n=an1
−9×x1361
Rewrite the expression
x136−9
Use b−a=−ba=−ba to rewrite the fraction
−x1369
3x23−x1369
Simplify the expression
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Evaluate
3x23
Use anm=nam to transform the expression
3x3
Simplify the radical expression
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Evaluate
x3
Rewrite the exponent as a sum
x2+1
Use am+n=am×an to expand the expression
x2×x
The root of a product is equal to the product of the roots of each factor
x2×x
Reduce the index of the radical and exponent with 2
xx
3xx
3xx−x1369
Use anm=nam to transform the expression
3xx−13x69
Simplify
More Steps

Evaluate
−13x69
Multiply by the Conjugate
−13x6×13x7913x7
Calculate
−x913x7
3xx−x913x7
Reduce fractions to a common denominator
x3xx×x−x913x7
Write all numerators above the common denominator
x3xx×x−913x7
Solution
x3x2x−913x7
Show Solution

Find the roots
x=51326
Alternative Form
x≈1.750807
Evaluate
3x23−9x261×x−(21)
To find the roots of the expression,set the expression equal to 0
3x23−9x261×x−(21)=0
Find the domain
3x23−9x261×x−(21)=0,x>0
Calculate
3x23−9x261×x−(21)=0
Remove the unnecessary parentheses
3x23−9x261×x−21=0
Multiply
More Steps

Multiply the terms
9x261×x−21
Multiply the terms with the same base by adding their exponents
9x261−21
Subtract the numbers
More Steps

Evaluate
261−21
Reduce fractions to a common denominator
261−2×1313
Multiply the numbers
261−2613
Write all numerators above the common denominator
261−13
Subtract the numbers
26−12
Cancel out the common factor 2
13−6
Use b−a=−ba=−ba to rewrite the fraction
−136
9x−136
3x23−9x−136=0
Rewrite the expression
More Steps

Evaluate
−9x−136
Express with a positive exponent using a−n=an1
−9×x1361
Rewrite the expression
x136−9
Use b−a=−ba=−ba to rewrite the fraction
−x1369
3x23−x1369=0
Multiply both sides of the equation by LCD
(3x23−x1369)x136=0×x136
Simplify the equation
More Steps

Evaluate
(3x23−x1369)x136
Apply the distributive property
3x23×x136−x1369×x136
Simplify
3x23×x136−9
Multiply the terms
More Steps

Evaluate
3x23×x136
Use anm=nam to transform the expression
3x3×x136
Simplify the radical expression
3xx×x136
Calculate
3x1319x
3x1319x−9
Rewrite the expression
More Steps

Evaluate
x1319x
Use anm=nam to transform the expression
13x19×x
Simplify the radical expression
x13x6×x
Calculate the product
x26x25
3x26x25−9
3x26x25−9=0×x136
Any expression multiplied by 0 equals 0
3x26x25−9=0
Move the constant to the right-hand side and change its sign
3x26x25=9
Divide both sides of the equation by 3
x26x25=3
Raise both sides of the equation to the 26-th power to eliminate the isolated 26-th root
(x26x25)26=326
Evaluate the power
x51=326
Take the 51-th root on both sides of the equation
51x51=51326
Calculate
x=51326
Check if the solution is in the defined range
x=51326,x>0
Solution
x=51326
Alternative Form
x≈1.750807
Show Solution
