Introduction to Indices
Q1. Write each expression in expanded form and evaluate.
(a) 23 (b) 52 (c) 104 (d) 34 (e) 16
Q2. Write each expression using index notation.
(a) 2 × 2 × 2 × 2 (b) 7 × 7 (c) 10 × 10 × 10
(d) 4 × 4 × 4 × 4 × 4 (e) a × a × a × a
Q3. Identify the base and index in each expression.
(a) 63 (b) x5 (c) 10n (d) (2a)4
Q4. Calculate:
(a) 20 (b) 50 (c) 1000 (d) (−3)2 (e) (−2)3
Q5. A bacteria culture doubles every hour. Starting with 100 bacteria:
(a) How many bacteria after 1 hour? 1 mark
(b) How many after 4 hours? Write your answer using index notation. 1 mark
(c) How many after n hours? 1 mark
Q6. A square has side length 3 cm. A larger square has side length 32 cm.
(a) Find the area of each square. 1 mark
(b) How many times larger is the area of the larger square? 1 mark
(c) If a square has side length 33 cm, what is its area? 1 mark
Q7. Without calculating, determine which is larger: 210 or 102? Explain your reasoning. 2 marks
Q8. Investigate the pattern when powers of 2 are multiplied.
(a) Calculate 22 × 23. Write your answer as a single power of 2. 1 mark
(b) Calculate 24 × 25. Write your answer as a single power of 2. 1 mark
(c) Predict the result of 2a × 2b without calculating. 1 mark
(d) Test your prediction with 32 × 34. 1 mark
Answer Key
Q1. (a) 2×2×2=8 (b) 5×5=25 (c) 10×10×10×10=10000 (d) 3×3×3×3=81 (e) 1×1×1×1×1×1=1
Q2. (a) 24 (b) 72 (c) 103 (d) 45 (e) a4
Q3. (a) base 6, index 3 (b) base x, index 5 (c) base 10, index n (d) base 2a, index 4
Q4. (a) 1 (b) 1 (c) 1 (d) 9 (e) −8
Q5. (a) 200 (b) 100 × 24 = 1600 (c) 100 × 2n
Q6. (a) Small: 9 cm2; Large: 81 cm2 (b) 9 times larger (c) (33)2 = 36 = 729 cm2
Q7. 210 = 1024, 102 = 100. 210 is larger because repeated multiplication of 2 ten times produces a much larger result than 10×10.
Q8. (a) 4×8=32=25 (b) 16×32=512=29 (c) 2a+b (d) 9×81=729=36; 2+4=6, so 32+4=36
Work through this topic 1-on-1 with an experienced maths tutor.
Book a free session →