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Question
\frac{10.1038}{s^{4}}\times 1599-22-1418-8
Simplify the expression
\frac{80779881-7240000s^{4}}{5000s^{4}}
Evaluate
\frac{10.1038}{s^{4}}\times 1599-22-1418-8
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 1599-22-1418-8
Multiply the terms
More Steps
Multiply the terms
\frac{50519}{5000s^{4}}\times 1599
Multiply the terms
\frac{50519\times 1599}{5000s^{4}}
Multiply the terms
\frac{80779881}{5000s^{4}}
\frac{80779881}{5000s^{4}}-22-1418-8
Subtract the numbers
\frac{80779881}{5000s^{4}}-1448
Reduce fractions to a common denominator
\frac{80779881}{5000s^{4}}-\frac{1448\times 5000s^{4}}{5000s^{4}}
Write all numerators above the common denominator
\frac{80779881-1448\times 5000s^{4}}{5000s^{4}}
Solution
\frac{80779881-7240000s^{4}}{5000s^{4}}
Show Solutions
Find the excluded values
s=0
Evaluate
\frac{10.1038}{s^{4}}\times 1599-22-1418-8
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]{80779881\times 724^{3}}}{7240},s_{2}=\frac{\sqrt[4]{80779881\times 724^{3}}}{7240}
Alternative Form
s_{1}\approx -1.827642,s_{2}\approx 1.827642
Evaluate
\frac{10.1038}{s^{4}}\times 1599-22-1418-8
To find the roots of the expression,set the expression equal to 0
\frac{10.1038}{s^{4}}\times 1599-22-1418-8=0
The only way a power can not be 0 is when the base not equals 0
\frac{10.1038}{s^{4}}\times 1599-22-1418-8=0,s\neq 0
Calculate
\frac{10.1038}{s^{4}}\times 1599-22-1418-8=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 1599-22-1418-8=0
Multiply the terms
More Steps
Multiply the terms
\frac{50519}{5000s^{4}}\times 1599
Multiply the terms
\frac{50519\times 1599}{5000s^{4}}
Multiply the terms
\frac{80779881}{5000s^{4}}
\frac{80779881}{5000s^{4}}-22-1418-8=0
Subtract the terms
More Steps
Simplify
\frac{80779881}{5000s^{4}}-22
Reduce fractions to a common denominator
\frac{80779881}{5000s^{4}}-\frac{22\times 5000s^{4}}{5000s^{4}}
Write all numerators above the common denominator
\frac{80779881-22\times 5000s^{4}}{5000s^{4}}
Multiply the terms
\frac{80779881-110000s^{4}}{5000s^{4}}
\frac{80779881-110000s^{4}}{5000s^{4}}-1418-8=0
Subtract the terms
More Steps
Simplify
\frac{80779881-110000s^{4}}{5000s^{4}}-1418
Reduce fractions to a common denominator
\frac{80779881-110000s^{4}}{5000s^{4}}-\frac{1418\times 5000s^{4}}{5000s^{4}}
Write all numerators above the common denominator
\frac{80779881-110000s^{4}-1418\times 5000s^{4}}{5000s^{4}}
Multiply the terms
\frac{80779881-110000s^{4}-7090000s^{4}}{5000s^{4}}
Subtract the terms
More Steps
Evaluate
-110000s^{4}-7090000s^{4}
Collect like terms by calculating the sum or difference of their coefficients
\left(-110000-7090000\right)s^{4}
Subtract the numbers
-7200000s^{4}
\frac{80779881-7200000s^{4}}{5000s^{4}}
\frac{80779881-7200000s^{4}}{5000s^{4}}-8=0
Subtract the terms
More Steps
Simplify
\frac{80779881-7200000s^{4}}{5000s^{4}}-8
Reduce fractions to a common denominator
\frac{80779881-7200000s^{4}}{5000s^{4}}-\frac{8\times 5000s^{4}}{5000s^{4}}
Write all numerators above the common denominator
\frac{80779881-7200000s^{4}-8\times 5000s^{4}}{5000s^{4}}
Multiply the terms
\frac{80779881-7200000s^{4}-40000s^{4}}{5000s^{4}}
Subtract the terms
More Steps
Evaluate
-7200000s^{4}-40000s^{4}
Collect like terms by calculating the sum or difference of their coefficients
\left(-7200000-40000\right)s^{4}
Subtract the numbers
-7240000s^{4}
\frac{80779881-7240000s^{4}}{5000s^{4}}
\frac{80779881-7240000s^{4}}{5000s^{4}}=0
Cross multiply
80779881-7240000s^{4}=5000s^{4}\times 0
Simplify the equation
80779881-7240000s^{4}=0
Rewrite the expression
-7240000s^{4}=-80779881
Change the signs on both sides of the equation
7240000s^{4}=80779881
Divide both sides
\frac{7240000s^{4}}{7240000}=\frac{80779881}{7240000}
Divide the numbers
s^{4}=\frac{80779881}{7240000}
Take the root of both sides of the equation and remember to use both positive and negative roots
s=\pm \sqrt[4]{\frac{80779881}{7240000}}
Simplify the expression
More Steps
Evaluate
\sqrt[4]{\frac{80779881}{7240000}}
To take a root of a fraction,take the root of the numerator and denominator separately
\frac{\sqrt[4]{80779881}}{\sqrt[4]{7240000}}
Simplify the radical expression
More Steps
Evaluate
\sqrt[4]{7240000}
Write the expression as a product where the root of one of the factors can be evaluated
\sqrt[4]{10000\times 724}
\text{Write the number in exponential form with the base of }10
\sqrt[4]{10^{4}\times 724}
The root of a product is equal to the product of the roots of each factor
\sqrt[4]{10^{4}}\times \sqrt[4]{724}
\text{Reduce the index of the radical and exponent with }4
10\sqrt[4]{724}
\frac{\sqrt[4]{80779881}}{10\sqrt[4]{724}}
Multiply by the Conjugate
\frac{\sqrt[4]{80779881}\times \sqrt[4]{724^{3}}}{10\sqrt[4]{724}\times \sqrt[4]{724^{3}}}
The product of roots with the same index is equal to the root of the product
\frac{\sqrt[4]{80779881\times 724^{3}}}{10\sqrt[4]{724}\times \sqrt[4]{724^{3}}}
Multiply the numbers
More Steps
Evaluate
10\sqrt[4]{724}\times \sqrt[4]{724^{3}}
Multiply the terms
10\times 724
Multiply the terms
7240
\frac{\sqrt[4]{80779881\times 724^{3}}}{7240}
s=\pm \frac{\sqrt[4]{80779881\times 724^{3}}}{7240}
\text{Separate the equation into }2\text{ possible cases}
\begin{align}&s=\frac{\sqrt[4]{80779881\times 724^{3}}}{7240}\\&s=-\frac{\sqrt[4]{80779881\times 724^{3}}}{7240}\end{align}
Check if the solution is in the defined range
\begin{align}&s=\frac{\sqrt[4]{80779881\times 724^{3}}}{7240}\\&s=-\frac{\sqrt[4]{80779881\times 724^{3}}}{7240}\end{align},s\neq 0
Find the intersection of the solution and the defined range
\begin{align}&s=\frac{\sqrt[4]{80779881\times 724^{3}}}{7240}\\&s=-\frac{\sqrt[4]{80779881\times 724^{3}}}{7240}\end{align}
Solution
s_{1}=-\frac{\sqrt[4]{80779881\times 724^{3}}}{7240},s_{2}=\frac{\sqrt[4]{80779881\times 724^{3}}}{7240}
Alternative Form
s_{1}\approx -1.827642,s_{2}\approx 1.827642
Show Solutions
