Ncert Solutions For Class 7 Maths Ex 13.1

Ncert Solutions For Class 7 Maths Chapter 13 Ex 13.1

Q.1.Find the value of:

(i) 26

(ii) 93

(iii) 112

(iv) 54

Solution:

(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

 

Q.2. Express the following in exponential form:

(i) 6×6×6×6

Solution: 6×6×6×6=64

(ii) t×t

Solution: t×t=t2

(iii) b×b×b×b

Solution: b×b×b×b=b4

(iv) 5×5×7×7×7

Solution: 5×5×7×7×7=52×73

(v) 2×2×a×a

Solution: 2×2×a×a=22×a2

(vi) a×a×a×c×c×c×c×d

Solution: a×a×a×c×c×c×c×d=a3×c4×d

 

Q.3. Express each of the following numbers using exponential notation:

(i) 512

(ii) 343

(iii) 729

(iv) 3125

Solution:

(i) 512

512=2×2×2×2×2×2×2×2×2=29

(ii)343

343=7×7×7=73

(iii)729

729=3×3×3×3×3×3=36

(iv)3125

3125=5×5×5×5×5=55

 

Q.4. Identify the greater number, wherever possible, in each of the following:

(i) 43and34

(ii) 53or35

(iii) 28or82

(iv) 1002and2100

Solution:

(i)43=4×4×4=6434=3×3×3×3=81

Since 64<81

So, 34 is greater than 43.

 

(ii)53=5×5×5=12535=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=25682=8×8=64

Since 64<256

So, 28 is greater than 82.

 

(iv) 1002=100×100=10,0002100=2×2×2×2×2×..14times×.×2=16,384×..×2

So, 2100 is greater than 1002.

 

Q.5. Express each of the following as product of powers of their prime factors:

(i) 648

(ii) 405

(iii) 540

Solution:

(i)648

648=23×34

(ii)405

405=5×34

(iii)540

540=22×33×5

 

Q.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

Solution:

(i)2×103=2×10×10×10=2000

(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)53×33=5×5×5×3×3×3=675

(vii)24×32=2×2×2×2×3×3=144

(viii)32×104=3×3×10×10×10×10=90,000

 

Q.7.Simplify:

(i)(4)3

(ii)(3)×(2)3

(iii) (3)2×(5)2

(iv)(2)3×(10)3

Solution:

(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

 

Q.8.Compare the following numbers:

(i)2.7×1012;1.5×108

(ii)4×1014;3×1017

Solution:

(i)2.7×1012;1.5×108

On comparing the exponents of base 10,

2.7×1012>1.5×108

(ii)4×1014;3×1017

On comparing the exponents of base 10,

4×1014<3×1017

 

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