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Question
\frac{10.1038}{s^{4}}\times 1467-20-20886-7
Simplify the expression
\frac{74111373-104565000s^{4}}{5000s^{4}}
Evaluate
\frac{10.1038}{s^{4}}\times 1467-20-20886-7
Divide the terms
More Steps
Evaluate
\frac{10.1038}{s^{4}}
Convert the decimal into a fraction
More Steps
Evaluate
10.1038
Convert the decimal into a fraction
\frac{101038}{10000}
Reduce the fraction
\frac{50519}{5000}
\frac{\frac{50519}{5000}}{s^{4}}
Multiply by the reciprocal
\frac{50519}{5000}\times \frac{1}{s^{4}}
Multiply the terms
\frac{50519}{5000s^{4}}
\frac{50519}{5000s^{4}}\times 1467-20-20886-7
Multiply the terms
More Steps
Multiply the terms
\frac{50519}{5000s^{4}}\times 1467
Multiply the terms
\frac{50519\times 1467}{5000s^{4}}
Multiply the terms
\frac{74111373}{5000s^{4}}
\frac{74111373}{5000s^{4}}-20-20886-7
Subtract the numbers
\frac{74111373}{5000s^{4}}-20913
Reduce fractions to a common denominator
\frac{74111373}{5000s^{4}}-\frac{20913\times 5000s^{4}}{5000s^{4}}
Write all numerators above the common denominator
\frac{74111373-20913\times 5000s^{4}}{5000s^{4}}
Solution
\frac{74111373-104565000s^{4}}{5000s^{4}}
Show Solutions
Find the excluded values
s=0
Evaluate
\frac{10.1038}{s^{4}}\times 1467-20-20886-7
To find the excluded values,set the denominators equal to 0
s^{4}=0
Solution
s=0
Show Solutions
Find the roots
s_{1}=-\frac{\sqrt[4]{24703791\times 55768^{3}}}{278840},s_{2}=\frac{\sqrt[4]{24703791\times 55768^{3}}}{278840}
Alternative Form
s_{1}\approx -0.917539,s_{2}\approx 0.917539
Evaluate
\frac{10.1038}{s^{4}}\times 1467-20-20886-7
To find the roots of the expression,set the expression equal to 0
\frac{10.1038}{s^{4}}\times 1467-20-20886-7=0
The only way a power can not be 0 is when the base not equals 0
\frac{10.1038}{s^{4}}\times 1467-20-20886-7=0,s\neq 0
Calculate
\frac{10.1038}{s^{4}}\times 1467-20-20886-7=0
Divide the terms
More Steps
Evaluate
\frac{10.1038}{s^{4}}
Convert the decimal into a fraction
More Steps
Evaluate
10.1038
Convert the decimal into a fraction
\frac{101038}{10000}
Reduce the fraction
\frac{50519}{5000}
\frac{\frac{50519}{5000}}{s^{4}}
Multiply by the reciprocal
\frac{50519}{5000}\times \frac{1}{s^{4}}
Multiply the terms
\frac{50519}{5000s^{4}}
\frac{50519}{5000s^{4}}\times 1467-20-20886-7=0
Multiply the terms
More Steps
Multiply the terms
\frac{50519}{5000s^{4}}\times 1467
Multiply the terms
\frac{50519\times 1467}{5000s^{4}}
Multiply the terms
\frac{74111373}{5000s^{4}}
\frac{74111373}{5000s^{4}}-20-20886-7=0
Subtract the terms
More Steps
Simplify
\frac{74111373}{5000s^{4}}-20
Reduce fractions to a common denominator
\frac{74111373}{5000s^{4}}-\frac{20\times 5000s^{4}}{5000s^{4}}
Write all numerators above the common denominator
\frac{74111373-20\times 5000s^{4}}{5000s^{4}}
Multiply the terms
\frac{74111373-100000s^{4}}{5000s^{4}}
\frac{74111373-100000s^{4}}{5000s^{4}}-20886-7=0
Subtract the terms
More Steps
Simplify
\frac{74111373-100000s^{4}}{5000s^{4}}-20886
Reduce fractions to a common denominator
\frac{74111373-100000s^{4}}{5000s^{4}}-\frac{20886\times 5000s^{4}}{5000s^{4}}
Write all numerators above the common denominator
\frac{74111373-100000s^{4}-20886\times 5000s^{4}}{5000s^{4}}
Multiply the terms
\frac{74111373-100000s^{4}-104430000s^{4}}{5000s^{4}}
Subtract the terms
More Steps
Evaluate
-100000s^{4}-104430000s^{4}
Collect like terms by calculating the sum or difference of their coefficients
\left(-100000-104430000\right)s^{4}
Subtract the numbers
-104530000s^{4}
\frac{74111373-104530000s^{4}}{5000s^{4}}
\frac{74111373-104530000s^{4}}{5000s^{4}}-7=0
Subtract the terms
More Steps
Simplify
\frac{74111373-104530000s^{4}}{5000s^{4}}-7
Reduce fractions to a common denominator
\frac{74111373-104530000s^{4}}{5000s^{4}}-\frac{7\times 5000s^{4}}{5000s^{4}}
Write all numerators above the common denominator
\frac{74111373-104530000s^{4}-7\times 5000s^{4}}{5000s^{4}}
Multiply the terms
\frac{74111373-104530000s^{4}-35000s^{4}}{5000s^{4}}
Subtract the terms
More Steps
Evaluate
-104530000s^{4}-35000s^{4}
Collect like terms by calculating the sum or difference of their coefficients
\left(-104530000-35000\right)s^{4}
Subtract the numbers
-104565000s^{4}
\frac{74111373-104565000s^{4}}{5000s^{4}}
\frac{74111373-104565000s^{4}}{5000s^{4}}=0
Cross multiply
74111373-104565000s^{4}=5000s^{4}\times 0
Simplify the equation
74111373-104565000s^{4}=0
Rewrite the expression
-104565000s^{4}=-74111373
Change the signs on both sides of the equation
104565000s^{4}=74111373
Divide both sides
\frac{104565000s^{4}}{104565000}=\frac{74111373}{104565000}
Divide the numbers
s^{4}=\frac{74111373}{104565000}
\text{Cancel out the common factor }3
s^{4}=\frac{24703791}{34855000}
Take the root of both sides of the equation and remember to use both positive and negative roots
s=\pm \sqrt[4]{\frac{24703791}{34855000}}
Simplify the expression
More Steps
Evaluate
\sqrt[4]{\frac{24703791}{34855000}}
To take a root of a fraction,take the root of the numerator and denominator separately
\frac{\sqrt[4]{24703791}}{\sqrt[4]{34855000}}
Simplify the radical expression
More Steps
Evaluate
\sqrt[4]{34855000}
Write the expression as a product where the root of one of the factors can be evaluated
\sqrt[4]{625\times 55768}
\text{Write the number in exponential form with the base of }5
\sqrt[4]{5^{4}\times 55768}
The root of a product is equal to the product of the roots of each factor
\sqrt[4]{5^{4}}\times \sqrt[4]{55768}
\text{Reduce the index of the radical and exponent with }4
5\sqrt[4]{55768}
\frac{\sqrt[4]{24703791}}{5\sqrt[4]{55768}}
Multiply by the Conjugate
\frac{\sqrt[4]{24703791}\times \sqrt[4]{55768^{3}}}{5\sqrt[4]{55768}\times \sqrt[4]{55768^{3}}}
The product of roots with the same index is equal to the root of the product
\frac{\sqrt[4]{24703791\times 55768^{3}}}{5\sqrt[4]{55768}\times \sqrt[4]{55768^{3}}}
Multiply the numbers
More Steps
Evaluate
5\sqrt[4]{55768}\times \sqrt[4]{55768^{3}}
Multiply the terms
5\times 55768
Multiply the terms
278840
\frac{\sqrt[4]{24703791\times 55768^{3}}}{278840}
s=\pm \frac{\sqrt[4]{24703791\times 55768^{3}}}{278840}
\text{Separate the equation into }2\text{ possible cases}
\begin{align}&s=\frac{\sqrt[4]{24703791\times 55768^{3}}}{278840}\\&s=-\frac{\sqrt[4]{24703791\times 55768^{3}}}{278840}\end{align}
Check if the solution is in the defined range
\begin{align}&s=\frac{\sqrt[4]{24703791\times 55768^{3}}}{278840}\\&s=-\frac{\sqrt[4]{24703791\times 55768^{3}}}{278840}\end{align},s\neq 0
Find the intersection of the solution and the defined range
\begin{align}&s=\frac{\sqrt[4]{24703791\times 55768^{3}}}{278840}\\&s=-\frac{\sqrt[4]{24703791\times 55768^{3}}}{278840}\end{align}
Solution
s_{1}=-\frac{\sqrt[4]{24703791\times 55768^{3}}}{278840},s_{2}=\frac{\sqrt[4]{24703791\times 55768^{3}}}{278840}
Alternative Form
s_{1}\approx -0.917539,s_{2}\approx 0.917539
Show Solutions
