Exponents and Powers (Class 8)

What this worksheet covers

This is an eighteen-question practice worksheet on exponents and powers for Class 8, written to the pattern of the SOF International Mathematics Olympiad (IMO). It carries 24 marks and is designed to be attempted in 45 minutes, split across three sections — Mathematical Reasoning, Everyday Mathematics and Reasoning and Achievers Section. Every question is multiple choice with exactly one correct option, and every one comes with a fully worked solution rather than just an answer key — so a child who gets one wrong can see where the reasoning went astray instead of only learning that it did.

Skills your child practises

• Applied problem-solving on exponents and powers at Class 8 level
• Working accurately against a time limit, as the real paper demands
• Mathematical Reasoning questions in the olympiad format
• Everyday Mathematics and Reasoning questions in the olympiad format
• Achievers Section questions in the olympiad format
• Reading worked solutions to find the step that went wrong

How to use it

1. 1There are 18 questions in this worksheet. All questions are compulsory.
2. 2Each question has four options (A), (B), (C) and (D). Exactly one option is correct.
3. 3Questions 1–15 carry 1 mark each. Questions 16–18 (Achievers Section) carry 3 marks each.
4. 4There is no negative marking. Use of a calculator is not allowed.
5. 5Rough work may be done on the blank space at the side of each page.

Sample questions from this worksheet

A preview of what's inside Exponents and Powers (Class 8) — the PDF has the full set, and every question comes with a worked solution like these.

1. 1. The value of 3−2 is _______.

   • A{1/9}correct
   • B−6
   • C−9
   • D{1/6}
   Solution: A negative exponent means the reciprocal: a⁻ⁿ = 1 ÷ aⁿ.
   So 3⁻² = 1 ÷ 3² = {1/9}. Note that it is not negative.

2. 2. The number 1.5 × 108 written in usual form is _______.

   • A1,50,000
   • B15,00,000
   • C1,50,00,000
   • D15,00,00,000correct
   Solution: Moving the decimal point 8 places to the right gives 150000000, that is 15,00,00,000 (fifteen crore). This is roughly the distance in kilometres from the earth to the sun.

3. 3. Consider the following statements.(i) 2−3 is a negative number.(ii) (a × b)n = an × bn for all non-zero a and b.(iii) 00 is not defined.Which of the statements is/are correct?

   • A(i) and (ii) only
   • B(ii) and (iii) onlycorrect
   • C(i) and (iii) only
   • DAll three
   Solution: Statement (i) is false — a negative exponent gives a reciprocal, not a negative number: 2⁻³ = {1/8}, which is positive. Statement (ii) is true, for example (2 × 3)² = 36 = 2² × 3². Statement (iii) is true; 0⁰ is left undefined. Hence (ii) and (iii).