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About Powers & Roots — Class 8 IB

Work with integer exponents, square roots, cube roots, and laws of indices. This topic is part of the IB Class 8 mathematics syllabus (chapter: Unit 1). On this page you can practice 60 questions across three difficulty levels — 20 easy, 20 medium, and 20 hard — each with a visual step-by-step solution, plus a timed 35-question mastery test with a live leaderboard. Worked examples and sample questions from the topic are below.

Powers & Roots — solved examples for Class 8 IB

Example 1easy

What is the value of \(3^2\)?
  1. A)6
  2. B)9
  3. C)12
  4. D)27

Step-by-step solution

  1. To find \(3^2\), multiply 3 by itself.
    32=3×3=93^2 = 3 \times 3 = 9

Answer: 9

Example 2medium

Simplify \(2^3 \times 2^4\) using index laws.
  1. A)\(2^7\)
  2. B)\(2^{12}\)
  3. C)\(4^7\)
  4. D)\(2^1\)

Step-by-step solution

  1. Apply the product rule for exponents: \(a^m \times a^n = a^{m+n}\).
    23×24=23+4=272^3 \times 2^4 = 2^{3+4} = 2^7

Answer: \(2^7\)

Example 3hard

Simplify \(\dfrac{2^5 \times 2^3}{2^4}\).
  1. A)\(2^2\)
  2. B)\(2^4\)
  3. C)\(2^{12}\)
  4. D)\(2^{15}\)

Step-by-step solution

  1. Combine the numerator using the product rule.
    25×23=282^5 \times 2^3 = 2^8
  2. Then apply the quotient rule.
    2824=28−4=24=16\frac{2^8}{2^4} = 2^{8-4} = 2^4 = 16

Answer: \(2^4\)

Practice questions on Powers & Roots

  1. Q1.easy

    What is \(\sqrt{49}\)?
    1. A)5
    2. B)6
    3. C)7
    4. D)8
    Show answer

    Answer: 7

    Hint: Which number multiplied by itself gives 49?

  2. Q2.easy

    What is \(2^5\)?
    1. A)10
    2. B)16
    3. C)32
    4. D)64
    Show answer

    Answer: 32

    Hint: Multiply 2 by itself 5 times.

  3. Q3.easy

    What is \(\sqrt{144}\)?
    1. A)11
    2. B)12
    3. C)13
    4. D)14
    Show answer

    Answer: 12

    Hint: Think about which number squared gives 144.

  4. Q4.medium

    Simplify \(\dfrac{5^6}{5^2}\).
    1. A)\(5^3\)
    2. B)\(5^4\)
    3. C)\(5^8\)
    4. D)\(1^4\)
    Show answer

    Answer: \(5^4\)

    Hint: When dividing powers with the same base, subtract the exponents.

  5. Q5.medium

    Simplify \((3^2)^3\).
    1. A)\(3^5\)
    2. B)\(3^6\)
    3. C)\(9^3\)
    4. D)\(3^8\)
    Show answer

    Answer: \(3^6\)

    Hint: When raising a power to another power, multiply the exponents.

  6. Q6.medium

    Evaluate \(\sqrt{196}\).
    1. A)12
    2. B)13
    3. C)14
    4. D)15
    Show answer

    Answer: 14

    Hint: Try squaring numbers between 12 and 15 to find which gives 196.

  7. Q7.hard

    Simplify \(\dfrac{(3^2)^4}{3^5}\).
    1. A)\(3^2\)
    2. B)\(3^3\)
    3. C)\(3^6\)
    4. D)\(3^{11}\)
    Show answer

    Answer: \(3^3\)

    Hint: First use the power rule in the numerator, then the quotient rule.

  8. Q8.hard

    Evaluate \(\left(\dfrac{27}{8}\right)^{\frac{1}{3}}\).
    1. A)\(\dfrac{3}{2}\)
    2. B)\(\dfrac{9}{4}\)
    3. C)\(\dfrac{2}{3}\)
    4. D)\(\dfrac{27}{2}\)
    Show answer

    Answer: \(\dfrac{3}{2}\)

    Hint: A fractional exponent of 1/3 means taking the cube root.

  9. Q9.hard

    Simplify \(\sqrt{12} + \sqrt{27}\).
    1. A)\(5\sqrt{3}\)
    2. B)\(\sqrt{39}\)
    3. C)\(3\sqrt{3}\)
    4. D)\(7\sqrt{3}\)
    Show answer

    Answer: \(5\sqrt{3}\)

    Hint: Simplify each surd first, then combine like terms.

These are 9 of the 60 questions available for Powers & Roots. Start practicing above to unlock visual solutions, AI coaching, and the topic leaderboard — completely free.