simplify giving answer in the exponential form? 1) 5^17÷5^13=
Answers
Find the value of:
(i) 26 (ii) 93 (iii) 112 (iv) 54
Answer:
(i) 26 = 2 * 2 * 2 * 2 * 2 * 2 = 64
(ii) 93 = 9 * 9 * 9 = 729
(iii) 112 = 11 * 11 = 121
(iv) 54 = 5 * 5 * 5 * 5 = 625
Question 2:
Express the following in exponential form:
(i) 6 * 6 * 6 * 6 (ii) t * t (iii) b * b * b * b (iv) 5 * 5 * 7 * 7 * 7 (v) 2 * 2 * a * a
(vi) a * a * a * c * c * c * c * d
Answer:
(i) 6 * 6 * 6 * 6 = 64
(ii) t * t = t2
(iii) b * b * b * b = b4
(iv) 5 * 5 * 7 * 7 * 7 = 52 * 73
(v) 2 * 2 * a * a = 22 * a2
(vi) a * a * a * c * c * c * c * d = a3 * c4 * d
Question 3:
Express each of the following numbers using exponential notations:
(i) 512 (ii) 343 (iii) 729 (iv) 3125
Answer:
(i) 512 = 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 = 29

(ii) 343 = 7 * 7 * 7 = 73

(iii) 729 = 3 * 3 * 3 * 3 * 3 * 3 = 36

(iv) 3125 = 5 * 5 * 5 * 5 * 5 = 55

Question 4:
Identify the greater number, wherever possible, in each of the following:
(i) 43 and 34 (ii) 53 or 35 (iii) 28 or 82 (iv) 1002 or 2100 (v) 210 or 102
Answer:
(i) 43 = 4 * 4 * 4 = 64
34 = 3 * 3 * 3 * 3 = 81
Since 64 < 81
So, 34 is greater than 43
(ii) 53 = 5 * 5 * 5 = 125
35 = 3 * 3 * 3 * 3 * 3 = 243
Since 125 < 243
So, 35 is greater than 53
(iii) 28 = 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 = 256
82 = 8 * 8 = 64
Since, 256 > 64
Thus, 28 is greater than 82
(iv) 1002 = 100 * 100 = 10,000
2100 = 2 * 2 * 2 * 2 * 2 * …..14 times * ……… * 2 = 16,384 * ….. * 2
Since, 10,000 < 16,384 * ……. * 2
Thus, 2100 is greater than 1002.
(v) 210 = 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 = 1,024
102 = 10 * 10 = 100
Since, 1,024 > 100
Thus, 210 is greater than 102
Question 5:
Express each of the following as product of powers of their prime factors:
(i) 648 (ii) 405 (iii) 540 (iv) 3,600
Answer:
(i) 648 = 23 * 34

(ii) 405 = 5 * 34

(iii) 540 = 22 * 33 * 5

(iv) 3,600 = 24 * 32 * 52

Question 6:
Simplify:
(i) 2 * 103 (ii) 72 * 22 (iii) 23 * 5 (iv) 3 * 44 (v) 0 * 102
(vi) 52 * 33 (vii) 24 * 32 (viii) 32 * 104
Answer:
(i) 2 * 103 = 2 * 10 * 10 * 10 = 2,000
(ii) 72 * 22 = 7 * 7 * 2 * 2 = 196
(iii) 23 * 5 = 2 * 2 * 2 * 5 = 40
(iv) 3 * 44 = 3 * 4 * 4 * 4 * 4 = 768
(v) 0 * 102 = 0 * 10 * 10 = 0
(vi) 52 * 33 = 5 * 5 * 3 * 3 * 3 = 675
(vii) 24 * 32 = 2 * 2 * 2 * 2 * 3 * 3 = 144
(viii) 32 * 104 = 3 * 3 * 10 * 10 * 10 * 10 = 90,000
Question 7:
Simplify:
(i) (-4)3 (ii) (-3) * (-2)3 (iii) (-3)2 * (-5)2 (iv) (-2)3 * (-10)3
Answer:
(i) (-4)3 = (-4) * (-4) * (-4) = -64
(ii) (-3) * (-2)3 = (-3) * (-2) * (-2) * (-2) = 24
(iii) (-3)2 * (-5)2 = (-3) * (-3) * (-5) * (-5) = 225
(iv) (-2)3 * (-10)3 = (-2) * (-2) *(-2) *(-10) *(-10) *(-10) = 8000
Question 8:
Compare the following numbers:
(i) 2.7 * 1012; 1.5 * 108 (ii) 4 * 1014; 3 * 1017
Answer:
(i) 2.7 * 1012 and 1.5 * 108
On comparing the exponents of base 10,
2.7 * 1012 > 1.5 * 108
(ii) 4 * 1014 and 3 * 1017
On comparing the exponents of base 10,
4 * 1014 < 3 * 1017
Exercise 13.2
Question 1:
Using laws of exponents, simplify and write the answer in exponential form:
(i) 32 * 34 * 38 (ii) 615/610 (iii) a3 * a2 (iv) 7x * 72 (v) (52)3 /53
(vi) 25 * 55 (vii) a4 * b4 (viii) (34)3 (ix) (220/215) * 23 (x) 8t/82
Answer:
(i) 32 * 34 * 38 = 32+4+8 = 314 [Since am * an = am+n ]
(ii) 615/610 = 615-10 = 65 [Since am / an = am-n ]
(iii) a3 * a2 = a3+2 = a5 [Since am * an = am+n ]
(iv) 7x * 7
Answer: