HOMEWORK 2
RICKY NG
Question 2.1. Evaluate (−5)2 .
Solution. (−5)2 = (−5) × (−5) = 25 because negative times negative is positive.
Question 2.2. Evaluate −52 .
Solution. −52 = −1 × 52 = −25. Notice the difference between this and the previous
question.
Question 2.3. Evaluate (−5)3 .
Solution. (−5)3 = (−5) × (−5) × (−5) = 25 × (−5) = −125.
Question 2.4. Evaluate −53 .
Solution. −53 = −1 × 53 = −1 × 125 = −125. Again, note the difference between this
and the previous question.
Question 2.5. Simplify 38 · 3−5 .
Solution. Using the product rule, 38+(−5) = 33 .
Question 2.6. Simplify
79
.
7−5
Solution. Division of same bases = subtracting exponents: 79−(−5) = 79+5 = 714 .
Question 2.7. Simplify (6x−5 y 3 z 4 )2 .
Solution. Use the power rule and multiply each one individually:
(6x−5 y 3 z 4 )2 = (6 · x−5 · y 3 · z 4 )2
= 62 · (x−5 )2 · (y 3 )2 · (z 4 )2
= 36 · x−10 · y 6 · z 8
1
= 36 · 10 · y 6 · z 8
x
6 8
36y z
=
.
x10
1
5d−7e0
.
−3−1 d−2 e4
Question 2.8. Simplify
Solution. There are quite many ways to do this. I prefer the variable-by-variable, numberby-number way:
5d−7 e0
5
d−7 e0
=
×
×
−3−1 d−2 e4
−3−1 d−2 e4
Now rewrite
1
−3−1
= −31 = −3, and simplify
d−7
:
d−2
5d−7e0
1
= 5 × (−3) × d−7−(−2) × 4
−1
−2
4
−3 d e
e
1
= −15 × d−5 × 4
e
1
1
= −15 × 5 × 4
d
e
5
−15d
=
.
e4
Question 2.9. Simplify
√
32.
Solution. The quickest way is to see that
32 = 16 × 2.
Since 16 = 42 , we have
√
√
√
√
√
32 = 42 × 2 = 42 × 2 = 4 2.
Question 2.10. Simplify
Solution. We distribute
√
q
16
.
49
· to numerator and denominator:
r
√
16
16
4
=√ = .
49
7
49
2