164 Review Questions and Answers
Question 8-2
When we see a complicated expression raised to negative integer power, what must we watch
out for?Answer 8-2
We must be sure that the expression is not equal to 0, and can never attain a value of 0.
Otherwise, we’ll end up dividing by 0. That’s forbidden!Question 8-3
Suppose that we encounter these expressions. What restrictions must we place on x and y in
each case?(a) (x− 5)−^3 (b) (x+y)−^2
(c) (3xy)−^2 (d) (x−y)−^5Answer 8-3
We must be sure the expressions inside the parentheses can never equal 0. Here’s what we must
do to stay safe:(a) We can’t let x be equal to 5.
(b) We can’t let x be equal to −y.
(c) We can’t let either x or y be equal to 0.
(d) We can’t let x be equal to y.Question 8-4
What is meant by the square root of a number? The cube root? The 4th root? The nth root,
where n is a positive integer?Answer 8-4
The square root of a number is a quantity that gives us the original number when squared
(multiplied by itself or raised to the 2nd power). The cube root is a quantity that gives us the
original number when cubed (raised to the 3rd power). The 4th root is a quantity that gives
us the original number when raised to the 4th power. The nth root is a quantity that gives us
the original number when raised to the nth power.Question 8-5
Even-numbered roots can be ambiguous. For example, if we want to find the square root of
16, both 4 and −4 will work, because42 = 4 × 4 = 16and(−4)^2 = (−4)× (−4)= 16How can we prevent this sort of confusion?