In-text Questions — Exponential Notation — Power Play

1. 11 markGanita Prakash Cl-8 Part 1, Math Talk in §2.2

   Which expression describes the thickness of a sheet of paper after it is folded 10 times, if the initial thickness is v? (i) 10v (ii) 10 + v (iii) 2 × 10 × v (iv) 2¹⁰ (v) 2¹⁰v (vi) 10²v

   Hint. Each fold doubles the thickness, so 10 folds means multiplying by 2 ten times over, not adding or multiplying by 10 directly.

   Step 1 — Recall that each fold doubles the thickness. After 10 folds, the thickness has been multiplied by 2, ten times over: v × 2 × 2 × ... × 2 (10 twos), since each fold multiplies the current thickness by another factor of 2.

   Step 2 — Write this using exponents. v × 2¹⁰ = 2¹⁰v.

   ✦ Answer: (v) 2¹⁰v.

   Where students slip. Picking 10v or 10²v — folding doubles the thickness each time, so the factor is 2 raised to the power 10, not a plain multiple of 10.

2. 22 marksGanita Prakash Cl-8 Part 1, Math Talk in §2.2

   What is (−1)⁵? Is it positive or negative? What about (−1)⁵⁶?

   Hint. Track the sign through repeated multiplication — does an odd or even count of negative factors flip the sign?

   Step 1 — Work out (−1)⁵. Multiplying −1 by itself an odd number of times (5) leaves the result negative: (−1)⁵ = −1, since each pair of negatives cancels to positive but one negative is left over.

   Step 2 — Work out (−1)⁵⁶. Multiplying −1 by itself an even number of times (56) makes the result positive: (−1)⁵⁶ = 1.

   ✦ Answer: (−1)⁵ is negative; (−1)⁵⁶ is positive.

   Where students slip. Assuming any power of −1 is negative — the sign flips back to positive whenever the exponent is even, since the negative signs cancel out in pairs.

3. 31 markGanita Prakash Cl-8 Part 1, Math Talk in §2.2

   Is (−2)⁴ = 16? Verify.

   Hint. Multiply −2 by itself four times, keeping track of the sign at each step.

   Step 1 — Expand the power. (−2)⁴ = (−2) × (−2) × (−2) × (−2).

   Step 2 — Multiply step by step. (−2) × (−2) = 4; 4 × (−2) = −8; −8 × (−2) = 16.

   ✦ Answer: Yes, (−2)⁴ = 16, since the four negative signs cancel out in pairs.

   Where students slip. Stopping after computing (−2) × (−2) × (−2) = −8 and forgetting the fourth factor, which flips the sign back to positive.

Solutions written by the tuition.in editorial team and checked against the NCERT Class 8 Mathematics textbook Ganita Prakash Part 1, Reprint 2026-27 (hegp102.pdf). Questions are scattered as 'Math Talk'/'Try This' prompts through the running text, plus two formal 'Figure it Out' blocks. Every answer here is checked against the book's own printed answer key at the end of the chapter.. Questions are referenced from the NCERT textbook for identification.