# Solve by Factoring r^(4/7)=16

Move to the left side of the equation by subtracting it from both sides.
Rewrite as .
Rewrite as .
Since both terms are perfect squares, factor using the difference of squares formula, where and .
Simplify.
Rewrite as .
Rewrite as .
Factor.
Since both terms are perfect squares, factor using the difference of squares formula, where and .
Remove unnecessary parentheses.
If any individual factor on the left side of the equation is equal to , the entire expression will be equal to .
Set the first factor equal to and solve.
Set the first factor equal to .
Subtract from both sides of the equation.
Raise each side of the equation to the power to eliminate the fractional exponent on the left side.
The complete solution is the result of both the positive and negative portions of the solution.
First, use the positive value of the to find the first solution.
Next, use the negative value of the to find the second solution.
The complete solution is the result of both the positive and negative portions of the solution.
Set the next factor equal to and solve.
Set the next factor equal to .
Subtract from both sides of the equation.
Raise each side of the equation to the power to eliminate the fractional exponent on the left side.
Raise to the power of .
Set the next factor equal to and solve.
Set the next factor equal to .
Add to both sides of the equation.
Raise each side of the equation to the power to eliminate the fractional exponent on the left side.
Raise to the power of .
The final solution is all the values that make true.
Exclude the solutions that do not make true.
Solve by Factoring r^(4/7)=16