Class 8 Maths

Exponents and Power

Exercise 12.1

Question 1: Evaluate.

(i) 3–2

exponents power 1

(ii) (– 4)– 2

exponents power 2
exponents power 3

Answer: = 2²+3²+4² = 4+9+16 = 29




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

exponents power 4
exponents power 5
exponents power 6
exponents power 7

Alternate Method:

= -34 x 54 ÷34 (the power on 3 is even so -34 = 34)
=30 x 54=625
(iv) (3–7 ÷Answer: Using am÷ an = am-n
(3–7 ÷ 3–10) = 3-7+10 = 33
Hence, (3–7 ÷ 3–10) × 3–5

=33 x 3–5
Now, am x an = am+n
Hence, = 33 x 3–5
= 33-5 = 3-2

(v) 2– 3 × (–7)–3

Answer: 2– 3 × (–7)–3

exponents power 8

Question 3: Find the value of.

(i) (3° + 4–1) × 22

Answer: (3° + 4–1) × 22

exponents power 9

(ii) (2–1 × 4–1) ÷ 2–2

exponents power 9

(iii) (3–1 + 4–1 + 5–1)0

Answer: aº=1
Hence, (3–1 + 4–1 + 5–1)0 = 1

exponents power 11

Question 4: Evaluate

exponents power 12

(ii) (5–1 × 2–1) × 6–1

exponents power 13

Question 5: Find the value of m for which 5m ÷ 5–3 = 55

Answer: am = am-n
Here, m-n = 5 and n = -3
So, m = 5+(-3)=2


Question 6: Evaluate

exponents power 14

Answer: (3-4)-1 = (-1)-1 =-1

exponents power 15

Question 7: Simplify.

(i) (25 x t-4) ÷ (5-3 x 10 x t-8)

Answer: (25 x t-4) ÷ (5-3 x 10 x t-8)
=(5² x t-4) ÷ (5-3 x 5 x 2 x t-8)
= 52+2 x t-4+8 ÷ 2
= 54 x t4 ÷ 2

(ii) (3-5 x 10-5 x 125) ÷ (5-7 x 6-5)

Answer:
= (3-5 x 5-5 x 2-5 x 53) ÷ (5-7 x 6-5)
= (3-5 x 5-5+3 x 2-5) ÷ (5-7 x 6-5)
= (3-5 x 5-2 x 2-5) ÷ (5-7 x 3-5 x 2-5)
= (3-5+5 x 5-2+7 x 2-5+5)
= (30 x 55 x 20)
=3125