CBSE Class 8 Maths Chapter 2: Power Play — Assertion & Reason
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The following Assertion and Reason questions are based on Chapter 2: Power Play from the NCERT Class 8 Mathematics textbook. Each question has four options - read both the Assertion (A) and Reason (R) carefully before selecting your answer.
How to attempt Assertion & Reason questions:
(a) Both A and R are true, and R is the correct explanation of A.
(b) Both A and R are true, but R is NOT the correct explanation of A.
(c) A is true, but R is false.
(d) A is false, but R is true.
(a) Both A and R are true, and R is the correct explanation of A.
(b) Both A and R are true, but R is NOT the correct explanation of A.
(c) A is true, but R is false.
(d) A is false, but R is true.
Assertion & Reason Questions
1
Assertion (A): Repeated doubling for n steps multiplies the starting quantity by 2 to the power n.
Reason (R): Each step introduces one additional factor of 2.
Reason (R): Each step introduces one additional factor of 2.
Answer: (a)
Both A and R are true, and R is the correct explanation of A. Exponential notation records repeated multiplication.
2
Assertion (A): The expression 5 cubed means 5 x 5 x 5.
Reason (R): The expression 10 to the power 4 equals 10000.
Reason (R): The expression 10 to the power 4 equals 10000.
Answer: (b)
Both A and R are true, but R is NOT the correct explanation of A. Both are true, but the power of ten does not explain 5 cubed.
3
Assertion (A): For nonzero a, a squared times a cubed equals a to the power 5.
Reason (R): Multiplying same-base powers requires multiplying the exponents.
Reason (R): Multiplying same-base powers requires multiplying the exponents.
Answer: (c)
A is true, but R is false. The exponents are added: 2 + 3 = 5.
4
Assertion (A): The expression (a squared) cubed equals a to the power 5.
Reason (R): Raising a power to a power multiplies the exponents.
Reason (R): Raising a power to a power multiplies the exponents.
Answer: (d)
A is false, but R is true. The correct exponent is 2 x 3 = 6.
5
Assertion (A): For nonzero a, a to the power 7 divided by a cubed equals a to the power 4.
Reason (R): Dividing same-base powers subtracts the denominator exponent.
Reason (R): Dividing same-base powers subtracts the denominator exponent.
Answer: (a)
Both A and R are true, and R is the correct explanation of A. Seven minus three equals four.
6
Assertion (A): The product a cubed b cubed equals (ab) cubed.
Reason (R): The value 10 to the power 3 is 1000.
Reason (R): The value 10 to the power 3 is 1000.
Answer: (b)
Both A and R are true, but R is NOT the correct explanation of A. Both are true, but the power of ten does not explain the product identity.
7
Assertion (A): For nonzero a, a to the power 0 equals 1.
Reason (R): Every nonzero base to exponent zero equals 0.
Reason (R): Every nonzero base to exponent zero equals 0.
Answer: (c)
A is true, but R is false. The quotient a cubed/a cubed gives 1.
8
Assertion (A): Zero to the power 0 is treated exactly like every nonzero base to exponent zero in elementary exponent laws.
Reason (R): Division arguments for exponent zero require a nonzero base.
Reason (R): Division arguments for exponent zero require a nonzero base.
Answer: (d)
A is false, but R is true. The usual law explicitly excludes zero.
9
Assertion (A): For nonzero a, a to the power -3 equals 1/a cubed.
Reason (R): A negative exponent represents the reciprocal of the corresponding positive power.
Reason (R): A negative exponent represents the reciprocal of the corresponding positive power.
Answer: (a)
Both A and R are true, and R is the correct explanation of A. This definition extends the exponent laws consistently.
10
Assertion (A): The value 2 to the power -1 is 1/2.
Reason (R): The value 10 to the power -3 is 0.001.
Reason (R): The value 10 to the power -3 is 0.001.
Answer: (b)
Both A and R are true, but R is NOT the correct explanation of A. Both are true reciprocal powers, but the second does not explain the first.
11
Assertion (A): The value 3 to the power -2 is 1/9.
Reason (R): A negative exponent makes every power negative.
Reason (R): A negative exponent makes every power negative.
Answer: (c)
A is true, but R is false. It takes a reciprocal rather than changing the sign.
12
Assertion (A): The expression (-2) to the power 4 is -16.
Reason (R): An even power of a negative base is positive.
Reason (R): An even power of a negative base is positive.
Answer: (d)
A is false, but R is true. Four factors of -2 multiply to 16.
13
Assertion (A): Multiplying a decimal by 10 to the power n shifts its decimal point n places to the right.
Reason (R): Each multiplication by 10 changes every digit's place value by one position.
Reason (R): Each multiplication by 10 changes every digit's place value by one position.
Answer: (a)
Both A and R are true, and R is the correct explanation of A. Repeating the shift n times gives the rule.
14
Assertion (A): A number written as 4.2 x 10 to the power 5 equals 420000.
Reason (R): Scientific notation helps represent very large or very small numbers compactly.
Reason (R): Scientific notation helps represent very large or very small numbers compactly.
Answer: (b)
Both A and R are true, but R is NOT the correct explanation of A. Both are true, but compact notation's usefulness does not explain this particular product.
15
Assertion (A): In standard scientific notation, the coefficient is at least 1 and less than 10.
Reason (R): A coefficient of 42 is already in standard form.
Reason (R): A coefficient of 42 is already in standard form.
Answer: (c)
A is true, but R is false. It must be rewritten with an adjusted power of ten.
16
Assertion (A): The number 0.00056 is 5.6 x 10 to the power 4.
Reason (R): A small positive number less than 1 uses a negative power of 10 in scientific notation.
Reason (R): A small positive number less than 1 uses a negative power of 10 in scientific notation.
Answer: (d)
A is false, but R is true. It is 5.6 x 10 to the power -4.
17
Assertion (A): Exponential growth can become very large after surprisingly few repeated doublings.
Reason (R): The multiplier itself doubles at every step through powers of 2.
Reason (R): The multiplier itself doubles at every step through powers of 2.
Answer: (a)
Both A and R are true, and R is the correct explanation of A. Repeated multiplication grows faster than adding a fixed amount.
18
Assertion (A): The expression 2 to the power 10 is 1024.
Reason (R): The expression 10 squared is 100.
Reason (R): The expression 10 squared is 100.
Answer: (b)
Both A and R are true, but R is NOT the correct explanation of A. Both are true, but the second power does not explain the first.
19
Assertion (A): Exponent laws for multiplication do not apply directly to addition.
Reason (R): The expression a squared + a cubed always equals a to the power 5.
Reason (R): The expression a squared + a cubed always equals a to the power 5.
Answer: (c)
A is true, but R is false. Adding unlike powers is different from multiplying them.
20
Assertion (A): The value of a power depends only on its exponent and never on its base.
Reason (R): Different bases raised to the same exponent generally give different results.
Reason (R): Different bases raised to the same exponent generally give different results.
Answer: (d)
A is false, but R is true. For example, 2 squared and 3 squared are unequal.
❓ Frequently Asked Questions
What is covered in CBSE Class 8 Maths Chapter 2 Power Play?
This chapter covers all key topics from Power Play as per CBSE 2026-27 syllabus.
Is this Assertion & Reason useful for CBSE board exams?
Yes, designed for CBSE Class 8 board exam preparation covering the complete syllabus.
Are these CBSE Class 8 Maths Assertion & Reason updated for 2026-27?
Yes, all content at eBookPublisher is updated as per the latest 2026-27 CBSE syllabus.
How many chapters are in CBSE Class 8 Maths?
All chapters of CBSE Class 8 Maths are covered at eBookPublisher with free Assertion & Reason for each chapter.
Can I study Power Play online for free?
Yes, complete Assertion & Reason for Power Play is available free at eBookPublisher. Study online directly — no download needed.
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