Exponents and Powers

Express the following numbers in the standard form:
(i) 5985.3 (ii) 65,950
(iii) 3,430,000 (iv) 70,040,000,000

Write exponential form for 8 × 8 × 8 × 8 taking base as 2.

Express the following terms in the exponential form:

(i) (2 × 3)⁵                    (ii) (2a)⁴                     (iii) (– 4m)³

Can you tell which one is greater (5²) x 3 or (5²)³ ?

Express the following numbers as a product of powers of prime factors:
(i) 72 (ii) 432 (iii) 1000 (iv) 16000

Express 256 as a power 2.

Express the following numbers in standard form:

(i) 5, 00, 00, 000 (ii) 70, 00, 000

(iii) 3, 18, 65, 00, 000 (iv) 3, 90, 878

(v) 39087.8 (vi) 3908.78

Find the number from each of the following expanded forms:

(a) 8 x 104 + 6 x 103 + 0 x 102 + 4 x 101 + 5 x 100

(b) 4 x 105 + 5 x 103 + 3 x 102 + 2 x 100

(c) 3 x 104 + 7 x 102 + 5 x 100

(d) 9 x 105 + 2 x 102 + 3 x 101

Express each of the following as a product of prime factors only in exponential form:

(i) 108 x 192 (ii) 270

(iii) 729 x 64 (iv) 768

Say true or false and justify your answer:

(i) 10 x 1011 = 10011 (ii) 23 > 52

(iii) 23 x 32 = 65 (iv) 30 = (1000)0

Simplify and express each of the following in exponential form:

(i)  (ii)  (iii) 

(iv)  (v)  (vi) 20 + 30 + 40

(vii) 20 × 30 × 40 (viii) (30 + 20) × 50 (ix) 

(x)  (xi)  (xii) 

Compare the following numbers:

(i) 2.7 x 1012; 1.5 x 108

(ii) 4 x 1014; 3 x 1017

Simplify:

(i) (- 4)3 (ii) (- 3) x (- 2)3

(iii) (- 3)2 x (- 5)2 (iv)(- 2)3 x (-10)3

Simplify:

(i) 2 x 103 (ii) 72 x 22

(iii) 23 x 5 (iv) 3 x 44

(v) 0 x 102 ­­­­­ (vi) 52 x 33

(vii) 24 x 32 (viii) 32 x 104

Express each of the following as product of powers of their prime factors:

(i) 648 (ii) 405

(iii) 540 (iv) 3,600

Find the value of:

(i) 26 (ii) 93

(iii) 112 (iv)54