Exercise 6 Page 432

Solving a equation with an expression raised to a rational exponent usually involves three main steps.

1. Isolate the expression raised to a rational exponent on one side of the equation.
2. Raise each side of the equation to a power equal to the reciprocal of the rational exponent.
3. Solve the resulting equation. Remember to check your results!

Now we can analyze the given equation. (x-5)^(13)-4=-2 First, let's isolate the expression raised to a rational exponent, (x-5)^(13), on one side of the equation.

In order to remove the 13 power, or cube root, we will raise each side of the equation to the power of 3.

Next, we will check the solution by substituting 13 for x into the original equation. If the substitution produces a true statement, we know that our answer is correct. If it does not, then it is an extraneous solution.

Because our substitution produced a true statement, we know that our answer, x=13, is correct.