Question
Mathematics Question on Laws of Exponents
Simplify and express the result in power notation with positive exponent.
- (−4) 5 ÷ (−4) 8
- (231) 2
- (−3) 4 × (35) 4
- (3 -7 ÷ 3 -10) × 3 -5
- 2 -3 × (−7) -3
Answer
(i) (−4)5 ÷ (−4)8
Since anam= am − n
(−4)5 ÷ (−4)8 = (−4)8(−4)5= (−4)5−8
(−4)−3
=(−4)31
(ii) (231)2
Since, (am)n = amn
⇒(231)2
=261
(iii) (−3)4 ×(35)4
We know that am × bm =(ab)m and (ba)m = bmam where a & b are non-zero integers and m is an integer
⇒ (−3)4 ×(35)4
⇒(−1×3)4×3454
⇒ (−1)4 × 54
= 54 [∵(−1)4 = 1]
(iv)(3−7 ÷ 3−10) × 3−5
We know. anam= 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 =321
(v) 2−3 × (−7)−3
We know that, am × bm = (ab)m
2−3 × (−7)−3
= [2 × (−7)]−3
= (−14)−3
=(−14)31 [Since a−m = 1/am]