Mathematics 320 Worksheet Page 4
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1
2
3
4Now, we simply divide both sides by a to show that
1 = 2.
Answer.
(1) Everything is fine up to equation (??), but in the next step both sides of this equation
are divided by the quantity (b a). Since a = b, we have that (b a) is zero. Division
by zero is undefined, so this is a mistake and the proof is wrong.
Section 3.3
Exercises.
3
5
8
5
5
5
3
5
(1) If 7
7
= 7
, and 3
7
= 21
, then what does 7
3
equal? What rule could you
formulate for such problems?
3
2
(4 )
(2) Is it true that (4
)
= 3
? Explain. Find an example where
(
)
(a ) = a
.
Answers.
(1) There is no ”shortcut” for this problem. Although some people might prefer to write
3
2
3
5
it as 21
3
, the answer to 7
3
is still 343 243 = 83, 349. If the bases match,
exponents may be added. If the exponents match, then the bases may be multiplied.
But if neither matches, you have to perform the calculations as shown.
3
2
2
(4 )
1
(2) They are not equal, since (4
)
= 81
= 6561 and 3
= 3
6 = 43, 046, 721? For an
2
2
(2 )
4
example, consider (3
)
= 3
= 3
.
Department of Mathematics, Kansas State University
E-mail address: mbscott@math.ksu.edu
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