CLASS 8TH CHAPTER 12 – EXPONENTS AND POWERS NCERT SOLUTION

Exercise 12.1 | Class 8th Mathematics

1. Evaluate:
   (i) 3^-2
   (ii) (-4)^-2
   (iii) (12)^-5
   Solution:
   

2. Simplify and express the result in power notation with a positive exponent.

Solution:

3. Find the value of

Solution:

4.

Solution:

5. Find the value of m for which 5^m ÷ 5^-3 = 5⁵.
Solution:
5^m ÷ 5^-3 = 5⁵
⇒ 5^m-(-3) = 5⁵ [∵ a^m ÷ aⁿ = a^m-n]
⇒ 5^m+3 = 5⁵
Comparing the powers of equal bases, we have
m + 3 = 5
m = 5 – 3 = 2, i.e., m = 2

6. Evaluate:

Solution:

7. Simplify:

Solution:

Exercise 12.2 | Class 8th Mathematics

1. Express the following numbers in standard form:
   (i) 0.0000000000085
   (ii) 0.00000000000942
   (iii) 6020000000000000
   (iv) 0.00000000837
   (v) 31860000000
   Solution:
   

(v) 31860000000
= 3.186 × 10000000000
= 3.186 × 10¹⁰
Hence, the required standard from = 3.186 × 10¹⁰

2. Express the following numbers in usual form.
(i) 3.02 × 10^-6
(ii) 4.5 × 10⁴
(iii) 3 × 10^-8
(iv) 1.0001 × 10⁹
(v) 5.8 × 10¹²
(vi) 3.61492 × 10⁶
Solution:

3. Express the number appearing in the following statements in standard form.
(i) 1 micron is equal to 11000000 m.
(ii) Charge of an electron is 0.000,000,000,000,000,000,16 coulomb
(iii) Size of a bacteria is 0.0000005 m
(iv) Size of a plant cell is 0.00001275 m
(v) Thickness of a thick paper is 0.07 mm.
Solution:

4. In a stack there are 5 books each of thickness 20 mm and 5 paper sheets each of thickness 0.016 mm. What is the total thickness of the stack?
Solution:
Thickness of books = 5 × 20 = 100 mm
Thickness of 5 paper sheets = 5 × 0.016 mm = 0.080 mm.
Total thickness of the stack = 100 mm + 0.080 mm = 100.080 mm = 1.0008 × 10² mm

Extra Questions | Class 8th Mathametics

1. Find the multiplicative inverse of:
   (i) 3^-3
   (ii) 10^-10
   Solution:
   

2. Expand the following using exponents.
(i) 0.0523
(ii) 32.005
Solution:

3. Simplify and write in exponential form.

Solution:

4. Simplify the following and write in exponential form.

Solution:

5. Express 8^-4 as a power with the base 2.
Solution:
We have 8 = 2 × 2 × 2 = 2³
8^-4 = (2³)^-4 = 2^3×(-4) = 2^-12

6. Simplify the following and write in exponential form.
(i) (3⁶ ÷ 3⁸)⁴ × 3^-4
(ii) 127 × 3^-3
Solution:

7. Find the value of k if (-2)^k+1 × (-2)³ = (-2)⁷
Solution:
(-2)^k+1 × (-2)³ = (-2)⁷
⇒ (-2)^k+1+3 = (-2)⁷
⇒ (-2)^k+4 = (-2)⁷
⇒ k + 4 = 7
⇒ k = 3
Hence, k = 3.

8. Simplify the following:

Solution:

9. Find the value of [(−34)−2]2
Solution:

10. Write the following in standard form
(i) 0 0035
(ii) 365.05
Solution:

Exponents and Powers Class 8 Extra Questions Short Answer Type

11. Find the value of P if

Solution:

12.

Solution:

13. Find the value of x if

Solution:

⇒ 3 + x = 18 [Equating the powers of same base]
x = 18 – 3 = 15

14. Solve the following: (81)^-4 ÷ (729)^2-x = 9^4x
Solution:

15.

Solution:

16.

Solution:

17. Find x so that (-5)^x+1 × (-5)⁵ = (-5)⁷ (NCERT Exemplar)
Solution:
(-5)^x+1 × (-5)⁵ = (-5)⁷
(-5)^x+1+5 = (-5)⁷ {a^m × aⁿ = a^m+n}
(-5)^x+6 = (-5)⁷
On both sides, powers have the same base, so their exponents must be equal.
Therefore, x + 6 = 7
x = 7 – 6 = 1
x = 1.