Class 8 Maths Exponents and Powers – Notes & MCQs

Class 8 Maths Exponents and Powers – Notes & MCQs

Exponents and Powers – Quick Notes (Class 8 NCERT)

1. Definition:

An exponent or power of a number tells how many times the number is multiplied by itself.

  • Example: 23=2×2×2=82^3 = 2 \times 2 \times 2 = 823=2×2×2=8
  • Here, 2 = base, 3 = exponent

2. Laws of Exponents

LawExplanationExample
am⋅an=am+na^m \cdot a^n = a^{m+n}am⋅an=am+nMultiply → add exponents23⋅24=272^3 \cdot 2^4 = 2^723⋅24=27
am/an=am−na^m / a^n = a^{m-n}am/an=am−nDivide → subtract exponents57/53=545^7 / 5^3 = 5^457/53=54
(am)n=amn(a^m)^n = a^{mn}(am)n=amnPower of a power → multiply(32)4=38(3^2)^4 = 3^8(32)4=38
(ab)n=anbn(ab)^n = a^n b^n(ab)n=anbnPower of a product(2⋅3)2=22⋅32(2 \cdot 3)^2 = 2^2 \cdot 3^2(2⋅3)2=22⋅32
(a/b)n=an/bn(a/b)^n = a^n / b^n(a/b)n=an/bnPower of a quotient(2/5)3=23/53(2/5)^3 = 2^3 / 5^3(2/5)3=23/53
a0=1a^0 = 1a0=1Any non-zero number to power 0 = 170=17^0 = 170=1
a−n=1/ana^{-n} = 1 / a^na−n=1/anNegative exponent2−3=1/23=1/82^{-3} = 1 / 2^3 = 1/82−3=1/23=1/8

3. Scientific Notation:

  • Numbers written as a × 10^n, where 1≤a<101 ≤ a < 101≤a<10 and n is integer
  • Example: 4500 = 4.5×1034.5 × 10^34.5×103

4. Important Notes / Tips

  • Always simplify powers using laws before calculating.
  • Watch negative signs carefully in powers.
  • 0n=00^n = 00n=0 for n > 0, but 000^000 is undefined.
  • Negative exponent = reciprocal

Exponents and Powers – MCQ Q&A

  1. Q: 23=?2^3 = ?23=?
    A: 8
  2. Q: 50=?5^0 = ?50=?
    A: 1
  3. Q: 3−2=?3^{-2} = ?3−2=?
    A: 1/32=1/91/3^2 = 1/91/32=1/9
  4. Q: 23⋅24=?2^3 \cdot 2^4 = ?23⋅24=?
    A: 23+4=27=1282^{3+4} = 2^7 = 12823+4=27=128
  5. Q: 57/53=?5^7 / 5^3 = ?57/53=?
    A: 57−3=54=6255^{7−3} = 5^4 = 62557−3=54=625
  6. Q: (32)4=?(3^2)^4 = ?(32)4=?
    A: 32×4=38=65613^{2×4} = 3^8 = 656132×4=38=6561
  7. Q: (2×3)2=?(2×3)^2 = ?(2×3)2=?
    A: 22×32=4×9=362^2 × 3^2 = 4 × 9 = 3622×32=4×9=36
  8. Q: (4/5)3=?(4/5)^3 = ?(4/5)3=?
    A: 43/53=64/1254^3 / 5^3 = 64/12543/53=64/125
  9. Q: 05=?0^5 = ?05=?
    A: 0
  10. Q: 10310^3103 in standard form?
    A: 1000
  11. Q: Scientific notation of 0.00056?
    A: 5.6×10−45.6 × 10^{-4}5.6×10−4
  12. Q: 2−3=?2^{-3} = ?2−3=?
    A: 1/23=1/81 / 2^3 = 1/81/23=1/8
  13. Q: Multiply: 52×535^2 × 5^352×53
    A: 52+3=55=31255^{2+3} = 5^5 = 312552+3=55=3125
  14. Q: Divide: 86/828^6 / 8^286/82
    A: 86−2=84=40968^{6−2} = 8^4 = 409686−2=84=4096
  15. Q: (72)3=?(7^2)^3 = ?(72)3=?
    A: 72×3=767^{2×3} = 7^672×3=76
  16. Q: Negative exponent rule?
    A: a−n=1/ana^{-n} = 1 / a^na−n=1/an ✅
  17. Q: 00=?0^0 = ?00=?
    A: Undefined ✅
  18. Q: 10−2=?10^{-2} = ?10−2=?
    A: 0.01
  19. Q: Expand (2×5)3(2×5)^3(2×5)3
    A: 23×53=8×125=10002^3 × 5^3 = 8 × 125 = 100023×53=8×125=1000
  20. Q: Scientific notation of 89000?
    A: 8.9×1048.9 × 10^48.9×104