Practice Exercises
This is an open-book quiz. You may (and should) refer to the text as you solve these problems.
Don’t hurry! You’ll find worked-out answers in App. A. The solutions in the appendix may not
represent the only way a problem can be figured out. If you think you can solve a particular
problem in a quicker or better way than you see there, by all means try it!
- What happens when a negative number is raised to an even positive integer power? An
odd positive integer power?
- What happens if we
(a) Raise −2 to increasing integer powers, starting with 1?
(b) Do the same thing with a base of −1?
(c) Do the same thing with a base of −1/2?
- What happens if we
(a) Raise −2 to decreasing negative integer powers, starting with −1?
(b) Do the same thing with a base of −1?
(c) Do the same thing with a base of −1/2?
- Suppose we come across the following expression. We want to simplify it to a sum
of individual terms. How can we do this? Here’s a hint: Use the results of the final
“challenge” in Chap. 5.
(y+ 1)^2
- If we use the same technique as in the previous problem, we can also simplify the
following expression. How?
(y− 1)^2
- Use the GAOE rule to prove, in narrative form, that for any number a except 0, and for
any rational numbers p, q, and r
apaqar=a(p+q+r)
- Use the GMOE rule to prove, in the form of an S/R table, that for any number a except 0,
and for any rational numbers p, q, and r
[(ap)q]r=apqr
- Prove, in narrative form, that if x is any number except 0, and if r and s are rational
numbers, then
(xr)s= (xs)r
- Show that if you take the 4th root of any positive number and then square the result, it
is the same as taking the square root of the original number.
- Show that if you take the 6th power of any positive number and then take the cube root
of the result, it is the same as squaring the original number.
Practice Exercises 123
