Unit 11 · Class 7 IB MYP · MCQ Test
Exponents & Powers MCQ Test — Class 7 IB MYP
Practice 10 multiple-choice questions with instant answer reveal and explanations.
Exponents & Powers — MCQ Questions
1Which statement correctly explains the meaning of 5^3?
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Answer: 5 × 5 × 5
Hint: Remember that the exponent tells you how many times the base number is multiplied by itself.
Solution:
The expression 5^3 means the base number, 5, is multiplied by itself.
The exponent, 3, indicates that this multiplication happens 3 times.
Therefore, 5^3 = 5 × 5 × 5.
2What is the value of 2^5?
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Answer: 32
Hint: The exponent indicates how many times the base is multiplied by itself.
Solution:
The expression 2^5 means 2 multiplied by itself 5 times.
Calculate the product step-by-step.
2 × 2 = 4
4 × 2 × 2 × 2 = 8 × 2 × 2 = 16 × 2 = 32
3Simplify the expression: m^6 × m^2.
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Answer: m^8
Hint: When multiplying powers with the same base, you add their exponents.
Solution:
The bases are the same (m).
According to the product rule, when multiplying powers with the same base, we add the exponents.
So, m^6 × m^2 = m^(6+2). — a^m × a^n = a^(m+n)
m^(6+2) = m^8.
4A storage facility in Rotterdam measures the number of identical containers in a stack. If each stack has 7^3 containers and there are 7^2 such stacks arranged in a row, how many containers are there in total? Express your answer in index notation.
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Answer: 7^5
Hint: When you have multiple stacks, you multiply the number of containers per stack by the number of stacks. Apply the product rule for exponents.
Solution:
Number of containers per stack = 7^3.
Number of stacks = 7^2.
Total containers = (containers per stack) × (number of stacks) = 7^3 × 7^2.
Using the product rule (add exponents): 7^(3+2) = 7^5.
5Simplify the expression: p^8 ÷ p^3.
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Answer: p^5
Hint: When dividing powers with the same base, you subtract the exponents.
Solution:
The bases are the same (p).
According to the quotient rule, when dividing powers with the same base, we subtract the exponents.
So, p^8 ÷ p^3 = p^(8-3). — a^m ÷ a^n = a^(m-n)
p^(8-3) = p^5.
6Alex was simplifying the expression 8^7 ÷ 8^2 and wrote: 8^7 ÷ 8^2 = 8^(7 ÷ 2) = 8^3.5. What was Alex's mistake?
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Answer: Alex should have subtracted the exponents instead of dividing them.
Hint: Recall the rule for dividing powers with the same base. Is it addition, subtraction, multiplication, or division of exponents?
Solution:
The rule for dividing powers with the same base (quotient rule) states that you subtract the exponents.
The correct simplification would be 8^(7-2) = 8^5.
Alex incorrectly divided the exponents (7 ÷ 2) instead of subtracting them.
7Simplify the expression: (y^3)^4.
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Answer: y^12
Hint: When raising a power to another power, you multiply the exponents.
Solution:
The expression is a power raised to another power.
According to the power of a power rule, we multiply the exponents.
So, (y^3)^4 = y^(3 × 4). — (a^m)^n = a^(m×n)
y^(3 × 4) = y^12.
8Which of the following expressions is equivalent to b^12?
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Answer: (b^2)^6
Hint: Test each option using the exponent rules (product rule, quotient rule, power of a power rule) to see which one simplifies to b^12.
Solution:
Evaluate each option using exponent rules:
Option A: (b^6)^6 = b^(6 × 6) = b^36. (Incorrect)
Option B: b^4 × b^3 = b^(4+3) = b^7. (Incorrect)
Option C: (b^2)^6 = b^(2 × 6) = b^12. (Correct)
Option D: b^10 ÷ b^2 = b^(10-2) = b^8. (Incorrect)
9What is the value of (25)^0?
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Answer: 1
Hint: Any non-zero base raised to the power of zero always equals a specific value.
Solution:
The expression is (25)^0.
According to the zero exponent rule, any non-zero number raised to the power of zero equals 1. — a^0 = 1 (for a ≠ 0)
Therefore, (25)^0 = 1.
10Simplify the expression: (4^2 × 4^3) ÷ (4^5 × 9^0).
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Answer: 1
Hint: Apply the product rule first for terms with the same base, then the zero exponent rule, and finally the quotient rule.
Solution:
Simplify the numerator using the product rule: 4^2 × 4^3 = 4^(2+3) = 4^5.
Simplify 9^0 using the zero exponent rule: 9^0 = 1.
The expression becomes 4^5 ÷ (4^5 × 1), which simplifies to 4^5 ÷ 4^5.
Using the quotient rule: 4^(5-5) = 4^0 = 1.
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Tips for Exponents & Powers MCQs
- 1Read each question carefully and identify what is being asked before looking at the options.
- 2Try to solve the problem mentally or on paper first, then match your answer with the options.
- 3Use elimination — rule out clearly wrong options to improve your chances even when unsure.
- 4Check units, signs, and edge cases — these are common traps in Exponents & Powers MCQs.
- 5Review your mistakes after completing the test to build lasting understanding.
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