Loading...

About Exponents and Powers — Class 7 Olympiad

Apply laws of exponents, work with powers of integers and rational numbers, and simplify complex expressions. This topic is part of the Olympiad Class 7 mathematics syllabus (chapter: Module 4). On this page you can practice 59 questions across three difficulty levels — 20 easy, 19 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 and Powers — solved examples for Class 7 Olympiad

Example 1easy

If 2^x = 16, what is the value of 2^(x+3)?
  1. A)A. 32
  2. B)B. 64
  3. C)C. 128
  4. D)D. 256

Step-by-step solution

  1. From the equation 2^x = 16, we know that 16 can be expressed as 2^4.
  2. So, 2^x = 2^4, which implies x = 4.
  3. Now substitute x = 4 into the expression 2^(x+3). This becomes 2^(4+3) = 2^7.
  4. Calculate 2^7: 2 × 2 × 2 × 2 × 2 × 2 × 2 = 128.

Answer: C. 128

Example 2medium

Simplify: (2^(a+3) × 4^(a-1)) / 8^(a-2)
  1. A)A. 2^(a+7)
  2. B)B. 2^7
  3. C)C. 2^(a+4)
  4. D)D. 2^(a-1)

Step-by-step solution

  1. Express all terms with base 2: 4 = 2^2 and 8 = 2^3.
  2. Substitute these into the expression: (2^(a+3) × (2^2)^(a-1)) / (2^3)^(a-2).
  3. Apply the power rule (x^m)^n = x^(m×n): (2^(a+3) × 2^(2a-2)) / 2^(3a-6).
  4. Apply the product rule x^m × x^n = x^(m+n) in the numerator: 2^((a+3) + (2a-2)) / 2^(3a-6) = 2^(3a+1) / 2^(3a-6).
  5. Apply the quotient rule x^m / x^n = x^(m-n): 2^((3a+1) - (3a-6)) = 2^(3a+1-3a+6) = 2^7.

Answer: B. 2^7

Example 3hard

Simplify the expression: (16^2 × 25^3) / (20^4)
  1. A)1/25
  2. B)1/5
  3. C)5
  4. D)25

Step-by-step solution

  1. Express all bases in terms of prime factors: 16 = 2^4, 25 = 5^2, 20 = 2^2 × 5.
  2. Substitute these into the expression and apply the power of a power rule (a^m)^n = a^(mn) and power of a product rule (ab)^n = a^n × b^n:
    ((24)2×(52)3)/((22×5)4)=(2(4×2)×5(2×3))/((22)4×54)=(28×56)/(28×54)( (2^4)^2 × (5^2)^3 ) / ( (2^2 × 5)^4 ) = ( 2^(4×2) × 5^(2×3) ) / ( (2^2)^4 × 5^4 ) = ( 2^8 × 5^6 ) / ( 2^8 × 5^4 )
  3. Apply the division rule a^m / a^n = a^(m-n) and the zero exponent rule a^0 = 1:
    2(8−8)×5(6−4)=20×52=1×25=252^(8-8) × 5^(6-4) = 2^0 × 5^2 = 1 × 25 = 25

Answer: 25

Practice questions on Exponents and Powers

  1. Q1.easy

    Simplify: [ (3^2)^3 × 3^0 ] / (3^4)
    1. A)A. 3^2
    2. B)B. 3^0
    3. C)C. 3^1
    4. D)D. 3^-1
    Show answer

    Answer: A. 3^2

    Hint: First, simplify the terms inside the brackets using the power of a power rule and the zero exponent rule. Then, apply the division rule.

  2. Q2.easy

    What is the unit digit of (-3)^2023?
    1. A)A. 1
    2. B)B. 3
    3. C)C. 7
    4. D)D. 9
    Show answer

    Answer: C. 7

    Hint: First, determine if the result will be positive or negative. Then, observe the pattern of the unit digits of powers of 3.

  3. Q3.easy

    If (2^a)^b = (2^3)^5, and a × b = 15, then what is the value of a + b?
    1. A)A. 8
    2. B)B. 16
    3. C)C. 18
    4. D)D. 30
    Show answer

    Answer: A. 8

    Hint: Recognize that the exponents must match on both sides of the equation. Consider the possible integer factors for a and b.

  4. Q4.medium

    If 3^(x+2) + 3^x = 270, what is the value of x?
    1. A)A. 1
    2. B)B. 2
    3. C)C. 3
    4. D)D. 4
    Show answer

    Answer: C. 3

    Hint: Look for common factors. Remember that 3^(x+2) can be expressed as a product involving 3^x.

  5. Q5.medium

    Which of the following numbers is the largest?
    1. A)A. 2^75
    2. B)B. 3^50
    3. C)C. 5^25
    4. D)D. 7^25
    Show answer

    Answer: B. 3^50

    Hint: To compare powers with different bases and exponents, try to make the exponents common by finding their HCF.

  6. Q6.medium

    A rare bacterial culture doubles its mass every 20 minutes. If a dish starts with 4 mg of bacteria, what will be its mass after 2 hours?
    1. A)A. 128 mg
    2. B)B. 256 mg
    3. C)C. 512 mg
    4. D)D. 1024 mg
    Show answer

    Answer: B. 256 mg

    Hint: Calculate the total number of doubling periods within the given time frame.

  7. Q7.hard

    Which of the following numbers is the largest: 2^60, 3^48, 4^36, 5^24?
    1. A)2^60
    2. B)3^48
    3. C)4^36
    4. D)5^24
    Show answer

    Answer: 3^48

    Hint: Find the greatest common divisor (GCD) of the exponents and rewrite each number with that GCD as the outermost exponent.

  8. Q8.hard

    If (2^(x+3)) × (4^(x-1)) = 2^(x+5), what is the value of x?
    1. A)0
    2. B)1
    3. C)2
    4. D)3
    Show answer

    Answer: 2

    Hint: Express all bases as powers of the same prime number. Then, use the laws of exponents to simplify both sides and equate the exponents.

  9. Q9.hard

    If 5^(x+2) - 5^(x) = 600, what is the value of 5^x?
    1. A)25
    2. B)50
    3. C)125
    4. D)100
    Show answer

    Answer: 25

    Hint: Factor out the common exponential term, 5^x, from the expression. Remember that 5^(x+2) can be written as 5^x × 5^2.

These are 9 of the 59 questions available for Exponents and Powers. Start practicing above to unlock visual solutions, AI coaching, and the topic leaderboard — completely free.