Simplify and express the result in power notation with positive exponent
(i) (−4) 5 ÷ (−4) 8 (ii) (1 / 23) 2 (iii) (−3) 4 × (5/3) 4
(iv) (3 -7 ÷ 3 -10) × 3 -5 (v) 2 -3 × (−7) -3
Solution:
The exponent of a number shows how many times the number is multiplied by itself.
(i) (−4)5 ÷ (−4)8
According to the rules of exponents,
we know that am/an = am − n where m and n are integers.
(−4)5 ÷ (−4)8 = (−4)5/(−4)8 = (−4)5−8
(−4)−3
= 1/(−4)3
(ii) (1/23)2
According to the rules of exponents,
we know that for any non-zero integer a, (am)n = amn
(1/23)2
= 1/26
(iii) (−3)4 × (5/3)4
According to the rules of exponents,
We know that am × bm =(ab)m and (a/b)m = am/bm where a & b are non-zero integers and m is an integer
(−3)4 × (5/3)4
(−1 × 3)4 × 54/34
(−1)4 × 54
= 54 [∵(−1)4 = 1]
(iv) (3−7 ÷ 3−10) × 3−5
According to the rules of exponents,
We know am/an = am − n and am × an = am + n
(3−7 ÷ 3−10) × 3−5 = (3−7−(−10)) × 3−5
= (3−7 + 10) × 3−5 = 33 × (3−5)
= 33 + (−5)
= 3−2 = 1/32
(v) 2−3 × (−7)−3
According to the rules of exponents,
We know that, am × bm = (ab)m
2−3 × (−7)−3
= [2 × (−7)]−3
= (−14)−3
= 1/(-14)3 [Since a−m = 1/am]
☛ Check: NCERT Solutions for Class 8 Maths Chapter 12
Video Solution:
Simplify and express the result in power notation with positive exponent. (i) (−4)⁵ ÷ (−4)⁸ (ii) (1 / 2³)² (iii) (−3)⁴ × (5/3)⁴ (iv) (3⁻⁷ ÷ 3⁻¹⁰) × 3⁻⁵ (v) 2⁻³ × (−7)⁻³
Class 8 Maths NCERT Solutions Chapter 12 Exercise 12.1 Question 2
Summary:
The following expressions are simplified and the result is expressed in power notation with a positive exponent. (i) (−4) 5 ÷ (−4) 8 = 1/(−4)3 (ii) (1 / 23) 2 = 1/26(iii) (−3) 4 × (5/3) 4 = 54 (iv) (3 -7 ÷ 3 -10) × 3-5 = 1/32 (v) 2 -3 × (−7) -3 = 1/(-14)3
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