# Solutions to Problem Set 23

Math 101-06

11-6-2017

[Fractional powers]

1. Simplify the expression and write your answer using positive powers. Assume the variables represent nonnegative numbers.

2. Simplify the expression and write your answer using positive powers. Assume the variables represent nonnegative numbers.

3. Simplify the expression and write your answer using positive powers. Assume the variables represent nonnegative numbers.

4. Simplify the expression and write your answer using positive powers. Assume the variables represent nonnegative numbers.

5. Solve for x:

Check:

The solution is 45.

6. Solve for x:

Check:

The solution is 16.

7. Solve for x:

A radical can't be negative, so the equation has no solutions.

8. Solve the following equation for x:

The possible solutions are and . Check:

checks and doesn't check.

The only solution is .

9. Solve the following equation for x:

The solution is .

10. Solve the following equation for x:

The solution is .

11. Solve .

Start by getting the square root term by itself:

Now square both sides and solve:

The possible solutions are and . Check them by plugging them into the left and right sides of the original equation:

The solutions are and .

12. Solve .

The possible solutions are and .. Check them by plugging them into the left and right sides of the original equation:

The only solution is .

He who has not lost his head over some things has no head to lose. - Jean-Paul Richter

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