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Page No 44:

Question 1:

Complete the table below.

  Sr. No.  Indices
(Numbers in index
     form)
 Base  Index  Multiplication form    Value
   (i)    34   3   4   3×3×3×3   81
   (ii)    163        
   (iii)     (-8)        2    
   (iv)         37×37×37×37   812401
   (v)   (-13)4        

Answer:

 

Sr. No. (Numbers in index form) Base Index Multiplication form Value
(i) 34 3 4 ××× 3 81
(ii) 163 16 3 16 × 16 × 16 4096
(iii) (−8)2 (−8) 2 (−8) × (−8) 64
(iv) 374 37 4 37×37×37×37 812401
(v) (−13)4 −13 4 (−13) × (−13) × (−13) × (−13) 28561
 

Page No 44:

Question 2:

Find the value.
 
(i) 210 (ii) 53    (iii) (-7)4    (iv) (-6)    (v) 93    (vi) 81  (vii) 453 (viii) -124
 
 

Answer:


i 210=2×2×2×2×2×2×2×2×2×2=1024
ii 53=5×5×5=125
iii -74 =-7×-7×-7×-7=2401
iv -63=-6×-6×-6=-216
v 93=9×9×9= 729
vi 81=8=8
vii 453=45×45×45=64125
viii -124=-12×-12×-12×-12=116



Page No 45:

Question 1:

Simplify.
 
(i) 74 × 72 (ii) (-11)5 × (-11)2 (iii) 673 × 675 


(iv) -325 × -323  (v) a16 × a7 (vi) P53 ×P57

Answer:

It is known that, am × an = am+n, where m and n are integers and a is a non-zero rational number.
i 74×72= 74+2=76
ii -115×-112=-115+2=-117
iii 673×675=673+5=678
iv -325×-323=-325+3=-328
v a16×a7=a16+7=a23
vi p53×p57=p53+7=p510



Page No 46:

Question 1:

Simplify.
(i) a6 ÷ a4    (ii) m5 ÷ m8 (iii) p3 ÷ p13 (iv) x10 ÷ x10

Answer:

It is known that, am ÷ an = amn, where m and n are integers and a is non-zero rational number.
i a6÷a4=a6-4=a2
ii m5÷m8=m5-8=m-3
iii p3÷p13=p3-13=p-10
iv x10÷x10=x10-10=x0=1     a0=1

Page No 46:

Question 2:

Find the value 

(i) (-7)12 ÷(-7)12    (ii) 75 ÷ 73   (iii) 453÷452   (iv) 47÷45

Answer:

It is known that, am ÷ an = amn, where m and n are integers and a is a non-zero rational number.
i -712÷-712=-712-12=-70=1     a0=1
ii 75÷73=75-3=72=7×7=49
iii 453÷452=453-2=451=45
iv 47÷45=47-5=42=4×4=16



Page No 48:

Question 1:

Simplify

(i)  151234   (ii) 34-2          (iii) 17-34    (iv)  25-2-3    (v) 654   

(vi)  6752   (vii) 23-45  (viii)  583-2   (ix) 3461   (x) 25-32

Answer:

It is known that, (am)n = amn, where m and n are integers and a is a non-zero rational number.
i 151234=15123×4=151212
ii 34-2=34×-2=3-8
iii 17-34=17-3×4=17-12
iv 25-2-3=25-2×-3=256
v 654=65×4=620
vi 6752=675×2=6710
vii 23-45=23-4×5=23-20
viii 583-2=583×-2=58-6
ix 3461=346×1=346
x 25-32=25-3×2=25-6

Page No 48:

Question 2:

Write the following numbers using positive indices.

(i) 27-2   (ii) 113-5  (iii) 16-3   (iv) y-4

Answer:

It is known that, a-m=1am where m is an integer and a is a non-zero rational number.
i 27-2=1272=722
ii 113-5=11135=3115
iii 16-3=1163=613=63
iv y-4=1y4=1y4



Page No 50:

Question 1:

Find the square root.
(i) 625   (ii) 1225   (iii) 289   (iv) 4096   (v) 1089

Answer:


(i) The prime factorization of 625 is,
625 = 5 × 5 ×  5 × 5
To find the square root, we will take one number from each pair and multiply.
625=5×5=25625=25
(ii) The prime factorization of 1225 is,
1225 = 5 × 5 × 7 × 7
To find the square root, we will take one number from each pair and multiply.
1225=5×7=351225=35
(iii) The prime factorisation of 289 is,
289 = 17 × 17
To find the square root, we will take one number from each pair and multiply.
289=17×17=17289=17
(iv) The prime factorization of 4096 is,
4096 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 â€‹× 2
To find the square root, we will take one number from each pair and multiply.
4096=2×2×2×2×2×2 = 644096=64
(v) The prime factorizationn of 1089 is,
1089 = 3 × 3 × 11 × 11
To find the square root, we will take one number from each pair and multipy.
1089=3×11=331089=33



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