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About Exponents & Powers — Class 8 CBSE

Apply laws of exponents including negative and zero exponents; standard form. This topic is part of the CBSE Class 8 mathematics syllabus (chapter: Chapter 2). 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.

Exponents & Powers — solved examples for Class 8 CBSE

Example 1easy

Simplify: 23×242^3 \times 2^4
  1. A)272^7
  2. B)2122^{12}
  3. C)474^7
  4. D)212^1

Step-by-step solution

  1. Using the law am×an=am+na^m \times a^n = a^{m+n}:
  2. 23×24=23+42^3 \times 2^4 = 2^{3+4}
    =27= 2^7

Answer: 272^7

Example 2medium

Simplify: 25×2−3×222^5 \times 2^{-3} \times 2^2
  1. A)242^4
  2. B)2102^{10}
  3. C)202^0
  4. D)232^3

Step-by-step solution

  1. 25×2−3×22=25+(−3)+22^5 \times 2^{-3} \times 2^2 = 2^{5+(-3)+2}
    =24= 2^4

Answer: 242^4

Example 3hard

Simplify: 25×34×432×32\frac{2^5 \times 3^4 \times 4}{3^2 \times 32}
  1. A)1818
  2. B)2727
  3. C)3636
  4. D)1212

Step-by-step solution

  1. 4=224 = 2^2 and 32=2532 = 2^5
  2. Numerator: 25×34×22=27×342^5 \times 3^4 \times 2^2 = 2^7 \times 3^4
  3. Denominator: 32×253^2 \times 2^5
  4. =27−5×34−2=22×32=4×9= 2^{7-5} \times 3^{4-2} = 2^2 \times 3^2 = 4 \times 9
    =36= 36

Answer: 3636

Practice questions on Exponents & Powers

  1. Q1.easy

    What is the value of 505^0?
    1. A)0
    2. B)1
    3. C)5
    4. D)Undefined
    Show answer

    Answer: 1

    Hint: Any non-zero number raised to the power 0 equals a specific value.

  2. Q2.easy

    Simplify: (32)3(3^2)^3
    1. A)353^5
    2. B)363^6
    3. C)939^3
    4. D)383^8
    Show answer

    Answer: 363^6

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

  3. Q3.easy

    What is 2−32^{-3}?
    1. A)−8-8
    2. B)−6-6
    3. C)18\frac{1}{8}
    4. D)16\frac{1}{6}
    Show answer

    Answer: 18\frac{1}{8}

    Hint: A negative exponent means take the reciprocal.

  4. Q4.medium

    Express 0.00056 in standard form (scientific notation).
    1. A)5.6×10−45.6 \times 10^{-4}
    2. B)56×10−556 \times 10^{-5}
    3. C)5.6×10−35.6 \times 10^{-3}
    4. D)0.56×10−30.56 \times 10^{-3}
    Show answer

    Answer: 5.6×10−45.6 \times 10^{-4}

    Hint: Move the decimal point to get a number between 1 and 10.

  5. Q5.medium

    Simplify: (35)−2\left(\frac{3}{5}\right)^{-2}
    1. A)925\frac{9}{25}
    2. B)259\frac{25}{9}
    3. C)−625\frac{-6}{25}
    4. D)53\frac{5}{3}
    Show answer

    Answer: 259\frac{25}{9}

    Hint: Negative exponent on a fraction means flip the fraction first.

  6. Q6.medium

    If 2x=322^x = 32, find xx.
    1. A)4
    2. B)5
    3. C)6
    4. D)3
    Show answer

    Answer: 5

    Hint: Express 32 as a power of 2.

  7. Q7.hard

    If 2a=82^{a} = 8 and 3b=813^{b} = 81, find the value of ab\frac{a}{b}.
    1. A)34\frac{3}{4}
    2. B)43\frac{4}{3}
    3. C)23\frac{2}{3}
    4. D)13\frac{1}{3}
    Show answer

    Answer: 34\frac{3}{4}

    Hint: Express 8 as a power of 2 and 81 as a power of 3.

  8. Q8.hard

    Simplify: (2−1+3−15−1)\left(\frac{2^{-1} + 3^{-1}}{5^{-1}}\right)
    1. A)256\frac{25}{6}
    2. B)56\frac{5}{6}
    3. C)65\frac{6}{5}
    4. D)16\frac{1}{6}
    Show answer

    Answer: 256\frac{25}{6}

    Hint: Convert all negative exponents to fractions first.

  9. Q9.hard

    Find xx if (37)2x+1=(73)3\left(\frac{3}{7}\right)^{2x+1} = \left(\frac{7}{3}\right)^{3}.
    1. A)−1-1
    2. B)−2-2
    3. C)11
    4. D)22
    Show answer

    Answer: −2-2

    Hint: Express (7/3)(7/3) as (3/7)−1(3/7)^{-1} to get the same base.

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