Class 8 Maths · Chapter 2
Short answer: Chapter 2 "Power Play" (Ganita Prakash Part 1, Class 8) exponents/powers, laws of exponents (product, quotient, power-of-power), zero aur negative exponents, aur standard form (scientific notation) sikhata hai — bade/chhote numbers ko compact aur simple tarike se likhne ka tareeka.
Ganita Prakash Part 1 ke Chapter 2, "Power Play", me hum exponents (powers) ki duniya me utarte hain — chhoti si notation jo bade se bade numbers ko simple form me express karne ki taakat rakhti hai. Ye chapter uss foundation pe khada hai jo Chapter 1 "A Square and A Cube" me bani thi, aur aage jaake "Fractions in Disguise" jaise chapters ke concepts ke liye base taiyaar karta hai. Real life me hum aksar bahut bade numbers dekhte hain — jaise ki galaxy ki distance, ya bahut chhote numbers — jaise ek virus ka size. Aise numbers ko baar-baar likhna mushkil hota hai, isliye exponents ka use hota hai. Ye chapter sikhata hai ki kaise laws of exponents ka use karke calculations fast aur accurate banayi ja sakti hain, aur numbers ko standard form (scientific notation) me kaise represent karte hain.
Chapter 2 Summary — 5 Minute Revision
Chapter 2 "Power Play" — jo Ganita Prakash Part 1 ka hissa hai (2026-27 session ke rationalised NCERT Class 8 Maths syllabus me, jisme total 14 chapters hain: Part 1 me 1-7 aur Part 2 me 8-14) — exponents ki full grammar sikhata hai: base-exponent notation, product/quotient/power-of-power laws, zero aur negative exponents, aur standard form me numbers likhna. Ye chapter Class 9-10 ke algebra aur science (physics/chemistry ke bade-chhote numbers) ke liye base taiyaar karta hai. Practice ke liye students ko chahiye ki negative aur zero exponent rules ko clearly samjhein, same-base condition ko exponent laws apply karte waqt hamesha check karein, aur standard form conversion ko regularly practice karein — kyunki ye concept aage 'Fractions in Disguise' aur higher-class science chapters me repeatedly use hota hai.In-Text Questions — Solutions
7^5 × 7^-2 ko simplify karo.
7^5 × 7^-2 = 7^(5-2) = 7^3 = 343
(2^3)^2 aur 2^(3^2) me kya farak hai?
(2^3)^2 me pehle 2^3 = 8, phir 8^2 = 64. Power of a power law se: (2^3)^2 = 2^6 = 64.
2^(3^2) me pehle 3^2 = 9, phir 2^9 = 512. Dono alag results hain — bracket ki position important hai.
0.000045 ko standard form me likho.
Decimal ko right side me 5 places move karna hoga taaki ek digit decimal se pehle aaye.
0.000045 = 4.5 × 10^-5
Exercise Questions — Solutions (Q1–Q6)
1. Likhiye ki 2 ki kaunsi power 1024 ke barabar hai?
2^n = 1024
1024 ko 2 se baar-baar divide karte hain: 1024 ÷ 2 = 512, 512 ÷ 2 = 256, 256 ÷ 2 = 128, 128 ÷ 2 = 64, 64 ÷ 2 = 32, 32 ÷ 2 = 16, 16 ÷ 2 = 8, 8 ÷ 2 = 4, 4 ÷ 2 = 2, 2 ÷ 2 = 1 — total 10 baar divide hua.
Isliye 2^10 = 1024
2. (-3)^4 aur -3^4 dono ki value nikaliye aur farak samjhaiye.
(-3)^4 me poora (-3) base hai aur power 4 (even) hai, isliye result positive aayega.
(-3)^4 = (-3) × (-3) × (-3) × (-3) = 81
-3^4 me sirf 3 base hai, minus sign baad me lagta hai (yaani -(3^4)).
-3^4 = -(3 × 3 × 3 × 3) = -81
Farak: bracket ka hona/na hona pura answer badal deta hai — 81 vs -81.
3. Simplify kijiye: 5^3 × 5^4 ÷ 5^2
Same base ho to exponents add/subtract hote hain.
5^3 × 5^4 = 5^(3+4) = 5^7
5^7 ÷ 5^2 = 5^(7-2) = 5^5
5^5 = 3125
4. Standard form me likhiye: 456,000,000
Number ko a × 10^n form me likhna hai jahan 1 ≤ a < 10.
456,000,000 = 4.56 × 100,000,000
456,000,000 = 4.56 × 10^8
5. Value nikaliye: 7^0 + 2^0 + 10^0
Zero law of exponents ke according, koi bhi non-zero number ki power 0 hamesha 1 hoti hai.
7^0 = 1, 2^0 = 1, 10^0 = 1
7^0 + 2^0 + 10^0 = 1 + 1 + 1 = 3
6. Negative exponent ko simplify kijiye: 2^-3
Negative exponent ka matlab hai reciprocal lena.
2^-3 = 1 / 2^3 = 1/8
Important Equations — Ek Nazar Me
Law | Formula | Example Product law (same base): a^m × a^n = a^(m+n) — e.g. 2^3 × 2^4 = 2^7 Quotient law (same base): a^m ÷ a^n = a^(m-n) — e.g. 5^6 ÷ 5^2 = 5^4 Power of a power: (a^m)^n = a^(m×n) — e.g. (3^2)^3 = 3^6 Power of a product: (ab)^n = a^n × b^n — e.g. (2×3)^2 = 2^2 × 3^2 Power of a quotient: (a/b)^n = a^n / b^n — e.g. (4/2)^2 = 4^2/2^2 Zero exponent: a^0 = 1 (a ≠ 0) — e.g. 15^0 = 1 Negative exponent: a^-n = 1/a^n — e.g. 4^-2 = 1/16 Standard form: N = a × 10^n (1 ≤ a < 10) — e.g. 93,000,000 = 9.3 × 10^7Common Mistakes — Yahan Marks Kat te Hain
- (-a)^n aur -a^n ko same samajh lena — bracket ka hona/na hona result completely badal deta hai, especially jab n even ho.
- Different bases ko exponent laws se add/multiply karne ki koshish karna — jaise 2^3 × 3^2 ko galat tarike se 6^5 bana dena. Laws of exponents SIRF same base pe apply hote hain.
- a^0 = 1 rule bhool jaana aur use 0 samajh lena — kisi bhi non-zero base ki zero power hamesha 1 hoti hai, chahe base kitna bhi bada ya chhota ho.
- Negative exponent ko negative number samajh lena — a^-n ka matlab number negative nahi, balki reciprocal (1/a^n) hota hai.
- Standard form likhte waqt decimal point ko galat direction me move karna — bade number me power positive hoti hai, chhote (decimal) number me power negative hoti hai, isme confusion aam hai.
- Power of a power law [(a^m)^n = a^(mn)] aur product law [a^m × a^n = a^(m+n)] ko mix kar dena — students exponents ko multiply karne ki jagah add kar dete hain ya vice versa.
Board-Style Important Questions
- Class 8 school-level assessment (Ganita Prakash based): 'Simplify 3^4 × 3^-2 ÷ 3^0 aur apna answer standard exponent form me likhiye' — is tarah ke practice questions periodic tests me common hain.
- Class 8 school-level assessment: '5,80,00,000 ko standard form me likhiye aur (-2)^5 ki value nikaliye' — combined numeric-plus-conceptual question ka common format.
- Class 8 school-level assessment: 'Laws of exponents ka use karke sabit kijiye ki (2/3)^3 × (2/3)^-1 = (2/3)^2' — verification-type question jo law-application test karta hai.
- Class 8 school-level assessment: 'a^m ÷ a^n = a^(m-n) ka use karke 10^7 ÷ 10^4 nikaliye aur uska standard form me matlab batayiye.'
- Class 8 school-level assessment: 'Negative aur zero exponent ke rules likhiye aur 6^0 + 4^-1 ki value ganit kijiye.'
Aksar Poochhe Jaane Wale Sawaal
Class 8 Maths chapter 'Power Play' kis topic pe based hai?
Ye chapter exponents aur powers pe based hai — jaise base aur exponent ka concept, laws of exponents (multiplication, division, power of a power), negative aur zero exponents, aur bade/chhote numbers ko standard form (scientific notation) me likhna. Ye Ganita Prakash Part 1 ka chapter hai (2026-27 session ke rationalised NCERT Class 8 Maths syllabus me).
NCERT ne Class 8 Maths ki new book ka naam kya rakha hai 2026-27 session ke liye?
2026-27 session se NCERT ne Class 8 Maths ki book ka naam 'Ganita Prakash' rakha hai, jo do parts me publish hoti hai — Part 1 (chapters 1 se 7) aur Part 2 (chapters 8 se 14). Ye purani single-book format se alag hai.
Ganita Prakash Part 1 aur Part 2 me kitne chapters hain?
Total 14 chapters hain — Part 1 me chapter 1 se 7 tak, aur Part 2 me chapter 8 se 14 tak. In chapters me topics jaise A Square and A Cube, Power Play, Proportional Reasoning, We Distribute Yet Things Multiply, Fractions in Disguise, Tales by Dots and Lines aur Number Play shamil hain.
Negative exponent ka rule kya hai?
Agar koi number ki power negative hai, toh us number ko reciprocal me convert karke exponent ko positive kar dete hain. Jaise a^-n = 1/a^n (jahan a ≠ 0).
Standard form (scientific notation) kya hota hai aur kyu use karte hain?
Standard form me kisi bhi bade ya chhote number ko a × 10^n ke form me likhte hain jahan 1 ≤ a < 10. Ye bahut bade numbers (jaise distance between planets) ya bahut chhote numbers (jaise atom ka size) ko compact aur asaani se likhne ke liye use hota hai.
Kya is chapter me old NCERT ka koi topic drop hua hai?
Exact rationalised-out topic list official ncert.nic.in rationalisation PDF se cross-verify nahi ho payi is session me, isliye ye claim yahan nahi banayi ja rahi — evidence na hone par estimate nahi kiya gaya hai.
Class 8 Maths — Saare Chapters
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