Question

evaluate the following

1. 8-5

2. (-2)+4

3. (-3)+(-8)

4. 10)0+(-4)​

Answer 1

Answer:

Evaluate:

(i) 3-2 (ii) (-4)-2 (iii) (1/2)-5

Answer:

(i) 3-2 = 1/32 = 1/9 [a-m = 1/ am]

(ii) (-4)-2 = 1/42 = 1/16 [a-m = 1/ am]

(iii) (1/2)-5 = (2/1)5 = 25 = 32 [a-m = 1/ am]

Question 2:

Simplify and express the result in power notation with positive exponent:

(i) (-4)5 ÷ (-4)8 (ii) (1/23)2 (iii) (-3)4 * (5/3)4 (iv) (3-7 * 3-10) * 35

(v) 2-3 * (-7)3

Answer:

(i) (-4)5 ÷ (-4)8 = (-4)5-8 [am ÷ an = am-n]

= (-4)-3

= 1/(-4)3 [a-m = 1/ am]

= -1/64

(ii) (1/23)2 = 12/(23)2 [(a/b)m = am/bm]

= 1/ 23*2 [(am)n = am*n]

= 1/26

= 1/64

(iii) (-3)4 * (5/3)4 = (-3)4 * (54/34 ) [(a/b)m = am/bm]

= (3)4 * (54/34 ) [(-a)m = am when m is an even number]

= (3)4-4 * 54

= 54

(iv) (3-7 * 3-10) * 35 = 3-7-10+5 [am * an = am+n]

= 3-17+5

= 3-12

= 1/312 [a-m = 1/ am]

(v) 2-3 * (-7)-3 = 1/23 * 1/(-7)-3 [a-m = 1/ am]

= 1/{(-7)3 * 23 }

= 1/(-7 * 2)3 [am * bm = (a * b)m]

= 1/(-14)3

= -1/(14)3 [(-a)m = -am when m is an odd number]

Answer 2

Answer:

$1. \: 8 - 5$

$= 3$

$2.( - 2) + 4$

$= 2$

$3. (-3)+(-8)$

$= (-3) - 8$

$= - 11$

$4. (10)0+(-4)$

$10-4$

$= 6$