Exercise 11.1

Find the value

(i)26 = 2 × 2 × 2 × 2 × 2 × 2 =

(ii)93 = 9 × 9 × 9 =

(iii)112 = 11 × 11 =

(iv)54 = 5 × 5 × 5 × 5 =

Express the following in exponential form.

(i)6 × 6 × 6 × 6 = 6

(ii)t × t = t

(iii)b × b × b × b = b

(iv)5 × 5 × 7 × 7 × 7 = 5 7

(v)2 × 2 × a × a = 2 × a

(vi)a × a × a × c × c × c × c × d = a × c × d

Express each of the following numbers using exponential notation.

(i)512 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 2

(ii)343 = 7 × 7 × 7 = 7

(iii)729 = 3 × 3 × 3 × 3 × 3 × 3 = 3

(iv)3125 = 5 × 5 × 5 × 5 × 5 =

Identify the greater number, wherever possible, in each of the following?

(i)43 or 34 = 43 ><= 34

(ii)53 or 35 = 53 >=< 35

(iii)28 or 82 = 28 ><= 82

(iv)1002 or 2100 = 1002 ><= 2100

(v)210 or 102 = 210 ><= 102

5. Express each of the following as product of powers of their prime factors.

(i)648 = 2 × 3

(ii)405 = 3 × 5

(iii)540 = 2 × 3 × 5

(iv)3,600 = 2 × 3 × 5

Simplify.

(i)2 × 103 = 2 × ( × 10 × )

= 2 × =

(ii)72 × 22 = ( × 7) × ( × 2)

= × =

(iii)23 × 5 = (2 × × 2) × 5

= × =

(iv)3 × 44 = 3 × ( × 4 × 4 × )

= 3 × =

(v)0 × 102 = 0 × 10 × =

(vi)52 × 33 = (5 × ) × ( × 3 × 3)

= × 27 =

(vii)24 × 32 = (2 × 2 × × 2) × (3 × )

= × 9 =

(viii)32 × 104 = (3 × 3) × (10 × × 10 × )

= 9 × =

Simplify.

(i)−43 = (-4) × (-4) × () = 64-64-60

(ii)(-3) × −23 = (-3) × (-2) × () × (-2) = (-3) × () =

(iii)−32 × −52 = () × (-3) × (-5) × () = 9 × =

(iv)−23 × −103 = () × (-2) × (-2) × () × (-10) × (-10) = (-8) × (-10001000) =

Simplify.

(i)2.7 × 1012 ; 1.5 × 108

(ii)4 × 1014 ; 3 × 1017