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Answer:

An index number is a FIGURE reflecting price or quantity compared with a base value. The base value always has an index number of 100. The index number is then expressed as 100 times the ratio to the base value.⇒ Cost of LIVING index = ∑w∑I. w=10010441. 5=104.

Step-by-step explanation:

HOPE it helps U and mark this answer as brainliest answer

The short notation 104 stands for the product 10×10×10×10. Here ‘10’ is called the base and ‘4’ the exponent. The number 104 is read as 10 raised to the power of 4 or simply as the fourth power of 10. 104 is called the exponential form of 10,000.

The other portion of the chapter gives insight about Laws of exponents. This particular section is divided into several sub-sections:

Multiplying Powers with the Same Base

Dividing Powers with the Same Base

Taking Power of a Power

Multiplying Powers with the Same Exponents

Dividing Powers with the Same Exponents

Numbers with exponent zero

Once the student has come across various laws of exponents miscellaneous examples using the laws of exponents can be studied.

This is followed by Decimal Number System and expressing large numbers in the standard form.

Any number can be expressed as a decimal number between 1.0 and 10.0 including 1.0 MULTIPLIED by a power of 10. Such a form of a number is called its standard form.

The chapter includes 3 unsolved exercises and various solved examples.

The chapter comprises a summary in which all the important concepts of the chapter- Exponents and Powers are mentioned.

Page No 252:

Question 1:

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

Page No 252:

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

Page No 253:

Question 3:

Express the following numbers using exponential notation:

(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

Page No 253:

Question 4:

Identify the greater number, wherever possible, in each of the following?

(i) 43 or 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

Therefore, 34 > 43

(ii) 53 = 5 × 5 × 5 =125

35 = 3 × 3 × 3 × 3 × 3 = 243

Therefore, 35 > 53

(iii) 28 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 256

82 = 8 × 8 = 64

Therefore, 28 > 82

(iv)1002 or 2100

210 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 1024

2100 = 1024 × 1024 × 1024 × 1024 × 1024 × 1024 × 1024 × 1024 ×1024 × 1024

1002 = 100 × 100 = 10000

Therefore, 2100 > 1002

(v) 210 and 102

210 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 1024

102 = 10 × 10 = 100

Therefore, 210 > 102

Page No 253:

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 = 2 × 2 × 2 × 3 × 3 × 3 × 3 = 23. 34

(ii) 405 = 3 × 3 × 3 × 3 × 5 = 34 . 5

(iii) 540 = 2 × 2 × 3 × 3 × 3 × 5 = 22. 33. 5

(iv) 3600 = 2 × 2 × 2 × 2 × 3 × 3 × 5 × 5 = 24. 32. 52

Page No 253:

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 × 1000 = 2000

(ii) 72 × 22 = 7 × 7 × 2 × 2 = 49 × 4 = 196

(iii) 23 × 5 = 2 × 2 × 2 × 5 = 8 × 5 = 40

(iv) 3 × 44 = 3 × 4 × 4 × 4 × 4 = 3 × 256 = 768

(v) 0 × 102 = 0 × 10 × 10 = 0

(vi) 52 × 33 = 5 × 5 × 3 × 3 × 3 = 25 × 27 = 675

(vii) 24 × 32 = 2 × 2 × 2 × 2 × 3 × 3 = 16 × 9 = 144

(viii) 32 × 104 = 3 × 3 × 10 × 10 × 10 × 10 = 9 × 10000 = 90000

Page No 253:

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) = 9 × 25 = 225

(iv) (−2)3 × (−10)3 = (−2) × (−2) × (−2) × (−10) × (−10) × (−10)

= (−8) × (−1000) = 8000

Page No 253:

Question 8:

Compare the following numbers:

(i) 2.7 × 1012; 1.5 × 108

(ii) 4 × 1014; 3 × 1017

ANSWER:

(i) 2.7 × 1012; 1.5 × 108

2.7 × 1012 > 1.5 × 108

(ii) 4 × 1014; 3 × 1017

3 × 1017 > 4 × 1014

Page No 260:

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) (vi) 25 × 55

(vii) a4 × b4 (viii) (34)3

(ix) (x) 8t ÷ 82

ANSWER:

(i) 32 × 34 × 38 = (3)2 + 4 + 8 (am × an = am+n)

= 314

(ii) 615 ÷ 610 = (6)15 − 10 (am ÷ an = am−n)

= 65

(iii) a3 × a2 = a(3 + 2) (am × an = am+n)

= a5

(iv) 7x + 72 = 7x + 2 (am × an = am+n)

(v) (52)3 ÷ 53

= 52 × 3 ÷ 53 (am)n = amn

= 56 ÷ 53

= 5(6 − 3) (am ÷ an = am−n)

= 53

(vi) 25 × 55

= (2 × 5)5 [am × bm = (a × b)m]

= 105

(vii) a4 × b4

= (ab)4 [am × bm = (a × b)m]

(viii) (34)3 = 34 × 3 = 312 (am)n = amn

(ix) (220 ÷ 215) × 23

= (220 − 15) × 23 (am ÷ an = am−n)

= 25 × 23

= (25 + 3) (am × an = am+n)

= 28

(x) 8t ÷ 82 = 8(t − 2) (am ÷ an = am−n)

Answer:

1/2

Step-by-step EXPLANATION:

ANSWER:

___1__ is the CORRECT answer

24300

hope it HELPS you❤ 66

Answer:

1176

Step-by-step explanation:

Then, as per the QUESTION 70% of BOYS = 70 NUMBER of girls = 30 Now, total number of students when the number of girls is 30 = 100 Then, total number of students when the number of girls is 504 = (100/30) × 504 = 1680 Total number of boys = 1680 – 504 = 1176

ANSWER:

Answer:

sorry PO hindi KO po ALAM eh

Step-by-step EXPLANATION:

pa brainleis po

salamat po

Answer:

thank you for your name and ADDRESS of the soul of the DAY

ANSWER:

IF P=-2

THEN

-3(-2)²+4(-2)+7

-3(4)+(-8)+7

-12-8+7

-13

HOPE U LIKE IT

Answer:

we will start by replacing the value of a

(5×2) + (3×2) -2

10 + 6 - 2

now we will FOLLOW the bodmas

(10 +6 ) -2

16 -2

=14

HOPE this might help you

ANSWER:

where is DIAGRAM to answer

Step-by-step explanation:

35+25+40=100/2=50

means 50 FAMILY is

ANSWER:

HOPE you GOT your answer ☺

ANSWER:

+ panch

Step-by-step EXPLANATION:

THEREFORE HENCE prooved

PAGALO PADAHI KRO

ssssssssssssssssssssssss

ANSWER:

X+36= -226

X= -226-36(PLUS CHANGES 2 MINUS WHILE CHANGING SIDES)

X= -262

HAPPY 2 HELP :)

MARK AS BRAINLIEST

Step-by-step explanation:

ANSWER:

SIDE of the second TRIANGLE is equal to 2 CM

Step-by-step explanation:

8*a*B*2-12*a*2*b is your ANSWER

ANSWER:

When X = 0 ,then Y = 3,When x=1, then y= 5+3=8

Answer:

i have made a NEW INTRO so PLZ check out the SHOWER and get a chance to get a polygon

ANSWER:

HEY MATE, I THINK this should be the CORRECT answer

Answer:

FOUGHT. God was a NICE way FOR1.

Answer:

4×-2 + -2×4

-8+ -8

-16

this is your answer

please MARK me as BRAINLEST.

Answer:

The TERM “bisexual” is used to describe a person who experiences emotional, romantic and/or sexual attractions to, or engages in romantic or sexual RELATIONSHIPS with, more than one sex or gender.

ANSWER:

8+3+7+2+11-

=9

Step-by-step EXPLANATION:

the answer is=9

Answer:

2MN+4MN+8MN+-6MN=SINCE ALL ARE LIKE TERMS

WE CAN ADD THEM

=8MN

HAPPY 2 HELP :)

MARK ME AS BRAINLIEST

Step-by-step EXPLANATION:

ANSWER:

132 is the answer

HOPE you FOUND this helpful

Step-by-step EXPLANATION:

Answer:

4

Step-by-step EXPLANATION:

PLEASE MARK me as BRAINLIEST

ANSWER:

SORRY don't KNOW the answer

Answer:

55%

is graphical REPRESENTATION of Air POLLUTION rate in Kerala and HIMACHAL PRADESH

Step-by-step EXPLANATION:

ANSWER:

-6

mark me as BRAINLIEST PLSS

ANSWER:

-1/4 is the Answer

Step-by-step EXPLANATION:

pls MARK me as brainlist and FOLLOW me

Step-by-step EXPLANATION:

ANSWER:

LET the number be x .

SEE the image

The number is 800

Answer:

for 150 students the RATION lasted for =60 days

after 12 days the ratio would last for= 60-12

48 days

now, for 150 students the ration LASTS for= 48days

for ONE student the ration will last for= 48×150

if 30 more JOIN the ration would last for= 48×150/180

=40 days

Step-by-step explanation:

<P>

p= RS .350,R=8%p.a T=3 1/2

years =7/2 years

SI = P .R. T/ 100

350 × 8 ×7/100×2

R.S. 98

and amount =p+S.I

RS. 350 +Rs.98 = Rs. 448

Answer:

3x7=21 BRUH

Step-by-step explanation:

3x7=21 , bruh

ANSWER:

I don't know if you have any QUESTIONS ask me to

Step-by-step explanation:

....

MARK me as BRAINLIST

your ANSWER in this ATTACHMENT PLEASE SEE it

hope.u LIKE

Answer:

it is 100 cm = 1 METER

please MARK it the BRAINLIEST

Answer:

PLEASE WRITE clearly . L don't understand

Step-by-step explanation:

please write in a CLEAR way

.

.

I don’t KNOW how to READ HINDI MARK me as WELL

ANSWER:

Why is distilled water USED in the BATTERIES and not the TAP water?

Answer:

Principal (P) = Rs. 24,000

Rate (R) = 7.5% P.A.

Time (T) = 4 Years

S.I. = (P × T × R)/100

= Rs. (24,000 × 4 × 7.5)/100

= Rs. 240 × 4 × 7.5

= 240 × 30 = Rs. 7200

Amount needed to clear the debt at the end of 4th year.

= Rs. 24000 + Rs. 7200 = Rs. 31200

Step-by-step explanation:

Answer:

A ductile failure is a TYPE of failure SEEN in malleable materials characterized by extensive PLASTIC deformation or necking. This usually occurs PRIOR to the actual failure of the MATERIAL. The term ductile rupture refers to the failure of highly ductile materials.

ANSWER:

Area of parallelogram which altitude corresponding to the SIDE of 12cm =area of parallelogram which altitude corresponding to 8cm  

altitude x BASE = altitude x base  

6cm x12cm = altitude x 8cm

altitude =9CM  

Step-by-step EXPLANATION:

Answer:

By USING EDL

a=bq+r

where a is > b

so a =867 and b=255

867=255×3+102

here r≠0 so a=255 and b=102

255=102×2+51

here r≠0 so a=102 and b=51

102=51×2+0

here r=0

so, Hcf of (867,255) is =51

Step-by-step EXPLANATION:

ANSWER:

OPTION C is the CORRECT answer