Chapter-7 Indices and Surds — Online MCQ Test
MATHS · Grade 10 · IGCSE cambridge
Practice Chapter-7 Indices and Surds with a free chapter-wise online MCQ test.
This chapter covers: Laws of indices negative and fractional powers and calculations in index form..
AI-generated questions from basic to board-exam level, with instant results and explanations.
Chapter-7 Indices and Surds — Important Questions & Answers
What is the value of 2^(-3)?
- A. -8
- B. 1/8
- C. -1/8
- D. 8
Answer: B. 1/8
A negative index means we take the reciprocal of the positive power: 2^(-3) = 1/(2^3) = 1/8.
A negative index means we take the reciprocal of the positive power: 2^(-3) = 1/(2^3) = 1/8.
Simplify: a^5 × a^3
- A. a^2
- B. a^8
- C. a^15
- D. 2a^8
Answer: B. a^8
Using the product rule of indices: a^m × a^n = a^(m+n), so a^5 × a^3 = a^(5+3) = a^8.
Using the product rule of indices: a^m × a^n = a^(m+n), so a^5 × a^3 = a^(5+3) = a^8.
Simplify: x^7 ÷ x^2
- A. x^5
- B. x^9
- C. x^(7/2)
- D. x^14
Answer: A. x^5
Using the quotient rule of indices: a^m ÷ a^n = a^(m-n), so x^7 ÷ x^2 = x^(7-2) = x^5.
Using the quotient rule of indices: a^m ÷ a^n = a^(m-n), so x^7 ÷ x^2 = x^(7-2) = x^5.
Calculate: 8^(2/3)
- A. 4
- B. 8/3
- C. 16
- D. 2
Answer: A. 4
8^(2/3) = (8^(1/3))^2 = (∛8)^2 = 2^2 = 4. Alternatively, 8^(2/3) = (8^2)^(1/3) = 64^(1/3) = 4.
8^(2/3) = (8^(1/3))^2 = (∛8)^2 = 2^2 = 4. Alternatively, 8^(2/3) = (8^2)^(1/3) = 64^(1/3) = 4.
Which statement is true about 5^(-2/3)?
- A. It equals -∛(25)
- B. It equals 1/∛(25)
- C. It equals (∛5)^2
- D. It is undefined
Answer: B. It equals 1/∛(25)
5^(-2/3) = 1/(5^(2/3)) = 1/((5^(1/3))^2) = 1/((∛5)^2) = 1/∛(25).
5^(-2/3) = 1/(5^(2/3)) = 1/((5^(1/3))^2) = 1/((∛5)^2) = 1/∛(25).