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Question
1\times v^{4}\times 107-196
Simplify the expression
107v^{4}-196
Evaluate
1\times v^{4}\times 107-196
Solution
More Steps
Evaluate
1\times v^{4}\times 107
Rewrite the expression
v^{4}\times 107
Use the commutative property to reorder the terms
107v^{4}
107v^{4}-196
Show Solutions
Find the roots
v_{1}=-\frac{\sqrt[4]{196\times 107^{3}}}{107},v_{2}=\frac{\sqrt[4]{196\times 107^{3}}}{107}
Alternative Form
v_{1}\approx -1.163371,v_{2}\approx 1.163371
Evaluate
1\times v^{4}\times 107-196
To find the roots of the expression,set the expression equal to 0
1\times v^{4}\times 107-196=0
Multiply the terms
More Steps
Multiply the terms
1\times v^{4}\times 107
Rewrite the expression
v^{4}\times 107
Use the commutative property to reorder the terms
107v^{4}
107v^{4}-196=0
Move the constant to the right-hand side and change its sign
107v^{4}=0+196
Removing 0 doesn't change the value,so remove it from the expression
107v^{4}=196
Divide both sides
\frac{107v^{4}}{107}=\frac{196}{107}
Divide the numbers
v^{4}=\frac{196}{107}
Take the root of both sides of the equation and remember to use both positive and negative roots
v=\pm \sqrt[4]{\frac{196}{107}}
Simplify the expression
More Steps
Evaluate
\sqrt[4]{\frac{196}{107}}
To take a root of a fraction,take the root of the numerator and denominator separately
\frac{\sqrt[4]{196}}{\sqrt[4]{107}}
Simplify the radical expression
\frac{\sqrt{14}}{\sqrt[4]{107}}
Multiply by the Conjugate
\frac{\sqrt{14}\times \sqrt[4]{107^{3}}}{\sqrt[4]{107}\times \sqrt[4]{107^{3}}}
Multiply the numbers
More Steps
Evaluate
\sqrt{14}\times \sqrt[4]{107^{3}}
\text{Use }\sqrt[n]{a}=\sqrt[mn]{a^m}\text{ to expand the expression}
\sqrt[4]{14^{2}}\times \sqrt[4]{107^{3}}
The product of roots with the same index is equal to the root of the product
\sqrt[4]{14^{2}\times 107^{3}}
Calculate the product
\sqrt[4]{196\times 107^{3}}
\frac{\sqrt[4]{196\times 107^{3}}}{\sqrt[4]{107}\times \sqrt[4]{107^{3}}}
Multiply the numbers
More Steps
Evaluate
\sqrt[4]{107}\times \sqrt[4]{107^{3}}
The product of roots with the same index is equal to the root of the product
\sqrt[4]{107\times 107^{3}}
Calculate the product
\sqrt[4]{107^{4}}
\text{Reduce the index of the radical and exponent with }4
107
\frac{\sqrt[4]{196\times 107^{3}}}{107}
v=\pm \frac{\sqrt[4]{196\times 107^{3}}}{107}
\text{Separate the equation into }2\text{ possible cases}
\begin{align}&v=\frac{\sqrt[4]{196\times 107^{3}}}{107}\\&v=-\frac{\sqrt[4]{196\times 107^{3}}}{107}\end{align}
Solution
v_{1}=-\frac{\sqrt[4]{196\times 107^{3}}}{107},v_{2}=\frac{\sqrt[4]{196\times 107^{3}}}{107}
Alternative Form
v_{1}\approx -1.163371,v_{2}\approx 1.163371
Show Solutions
