EXERCISE 1.1
1. State the base and index of each of the following expressions.
Group A
(a) 100
3
(b) 13
10
10
(c) (–12)
7
(d) 100
100
(e) x
10
(f) (–a)
10
2. Write each of the following numbers in the form of a .
(a) 5 to the power 10
(b) r to the power 2
(c)
to the power 4
(d) –2 to the 5   power
(e) x to the 6   power
(f) the 3   power of 10
(g) the 10   power of
(h) 3 x to the power n
(i) 2 × 2 × 2 × 2 × 2 × 2 × 2
(j) 0.5 × 0.5 × 0.5 × 0.5
(k)
(l) (–3) × (–3) × (–3) × (–3)
3. Calculate the following without using a calculator.
(a) 10
3
(b) (–3)
4
(c)
(d) 100
1
4. Simplify the following expressions, giving your answer using the index notation.
(a) x × x × x × x
(b) a  × a × a
3
6
(c) (–3) × 3 × 3
5. Find the value of each of the following expressions without using a calculator.
(a) 8 ×
(b) 0.2  × 10
2
3

(c) (–2)  × 5

3
3
(d) 2 × 3  × 2
2
3
3
4
(e) 3  + (–2)  + 5
2
2
3

(f) 3 × 10  + 10  + 3

3
2
3
Group B
6. Write each of the following numbers in the form of a n , where a is a real number and n is a
     positive integer.
(b) 100 000

(c) 16

(d) 625

7. Write each of the following in the form of a m × b n , where a , b are real numbers and m , n are
     positive integers.
(a) 12
(b) 36

(c) 63

(a) a  = 2 × 3  × 4
(e)–24

(f) 10 × 5 × 4

8. Find the value of the positive number a which satisfies the following equations. You may
     use a calculator.
3
3
(d) 64
(b) 4 × 25 × 3 = 3 a
2

(c) (2 a )  = 9 × 6 × 4

3
Group C
9. Find the values of n with satisfy the following equations.
(a) 12  = 9 × 4 × 3 × 16
n

(b) 2 × 5  = 10 × 125

n
10. (a) If n satisfies the equation 2  = n  , what is the value of n?
n
2
(b) If m and n are positive integers such that m  = n  , how are m and n related?
m
n
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