Exercise 4.1

1. Simplify and give reasons

i. 4−3

Solution:

ii. −27

Solution:

iii. 34−3

Solution:

iv. −3−4

Solution:

2. Simplify the following :

i. 124 × 125 × 126

Solution:

124 × 125 × 126 = 124+5+6 = 12151213

ii. −27 × −23 × −24

Solution:

−27 × −23 × −24 = −27+3+4−27×3×4 = −214−213

iii. 44 × 544

Solution:

44 × 544 = 4×544 = 54204 =

iv. 5−45−6 × 53

Solution:

5−45−6 × 53 = 5−4−−6 × 53 = 5254 × 535 = 52+352×3 = 5556

v. −34 × 74

Solution:

−34 × 74 = −3×74 = −214214

4. Simplify:

i. 40+5−1 × 52 × 8 × 13

Solution:

40+5−1 × 52 × 8 × 13 = ( + ) × × 8 × (1/3)

= × 25 ×

= 30×83 = 24032103

=

ii. 12−3 × 14−3 × 15−3

Solution:

12−3 × 14−3 × 15−3 = ()³ × ()³ × ()³

= 2×4×53 = 403603

=

iii. (2−1 + 3−1 + 4−1) × 34

Solution:

(2−1 + 3−1 + 4−1) × 34 = ( + + ) × (34) = () × (34) =

iv. 3−23×30−3−1

Solution:

3−23×30−3−1 = 3−2×3−1 × ( - ) = 3−2−1 × () = 3−3 × (2/3) = (1/) × (2/3) =

v. 1 + 2−1 + 3−1 + 40

Solution:

1 + 2−1 + 3−1 + 40 = 1 + + + 1

= 2 + 1/2 + 1/3 = 12+3+26 =

vi. 32−22

Solution:

32−22 = 32−2×2 = 32−432−3 = 234324 =

Therefore, the answer is 1681.

5. Simplify and give reason:

i. 32−22152

Solution:

32−22152 = 9−4152 = 5152 = 5×5212 = 25253 =

ii. 523×5456

Solution:

523×5456 = (52×352+3 × 54)/56 = (5654 × 54)/56

= 56+4/56 = 510/56 = 510−6 = 5453 =

6. Find the value of ‘n’ in each of the following :

i.233 × 235 = 23n−2

Solution:

233 × 235 = 23n−2

233+5233−5 = 23n−2

238232 = 23n−2

= -

n = 8 + 2

n =

ii. −3n+1 × −35 = −3−4

Solution:

−3n+1 × −35 = −3−4

−3n+1+5−3n+5 = −3−4

−3n+6 = −3−4

n + =

n = -4 - 6

n =

iii. 72n+149 = 73

Solution:

72n+1/49 = 73

72n+1/72 = 73

72n+1−272n+1+2 = 73

72n−172n+1 = 73

2n - 1 = 3

2n = 3 + 1

2n =

n = 42

n =

7. Find ‘x’ if 2−3 = 12x

Solution:

2−3 = 12x

2−3 = 2−x2x

= -x

x =

8. Simplify 34−245−3×35−2

Solution:

34−245−3×35−2 = 432342 / 543453 × 532352

= ()/() ×

= 16×64×259×125×9

= 45344434 ×

9. If m = 3 and n = 2 find the value of

i. 9m2 - 10n3

Solution:

Given m = 3 and n = 2, we substitute these values into the expression:

9m2 - 10n3 = 9×32 - 10×23 = 9() - 10()

= -

=

Therefore, the value of the expression is 1.

ii. 2m2n2

Solution:

Given m = 3 and n = 2, we substitute these values into the expression:

2m2n2 = 2×32×22

= 2()()

= ×

=

Therefore, the value of the expression is .

iii. 2m3 + 3n2 - 5m2n

Solution:

Given m = 3 and n = 2, we substitute these values into the expression:

2m3 + 3n2 - 5m2n = 2×33 + 3×22 - 5×32×2

= 2() + 3() - 5()()

= + -

= -

=

Therefore, the value of the expression is .

iv. mn - nm

Solution:

Given m = 3 and n = 2, we substitute these values into the expression:

mn - nm = 32 - 23

= -

=

Therefore, the value of the expression is 1.

10. Simplify and give reasons 47−5 × 74−7

Solution:

47−5 × 74−7

Since a−n = 1an and 1/a = a−1

= (745475) × (477747)

Since am+n = am × an

= 745 × 475744 × 472

Since am × bm = a×bm

= 745 × 475745 × 472

= 1545 × 472

= ×

=