ppt /exp.pptx/ NCERT based /Class 8/2024

PPt for class 8 ,NCERT

1. EXPONENTS AND POWERS

2. EXPONENTS AND POWERS VOCABULARY FACTORS - numbers that are multiplied together. BASE - the number being used as a factor. EXPONENT - tells how many times a number is used as a factor.

3. POWERS & EXPONENTS VOCABULARY POWER - a number that is expressed using exponents. SQUARED - a number that has an exponent of 2. CUBED - a number that has an exponent of 3.

4. EXPONENT FORM 2³ base exponent

5. FACTOR FORM 2³ = 2 x 2 x 2 factors

6. STANDARD FORM 2³ = 2 x 2 x 2 8 4 x 2

7. POWERS AND EXPONENTS 4³ 4 x 4 x 4 64 7² 7 x 7 49 m 5 m m m m m

8. Follow Order of Operations 5 + 3² - 8 5 + 3 x 3 - 8 5 + 9 - 8 14 - 8 6

9. What is the value of m ² + n ³ , if m=4 and n =5? 4 ² + 5³ 4 x 4 + 5 x 5 x 5 16 + 5 x 5 x 5 16 + 25 x 5 16 + 125 141

10. A light year is the distance light travels in one year. The Milky Way galaxy is about 100,000 light years wide. Write 100,000 as a power with 10 as the base. 10 5

11. Exponents power base exponent

12. Zero and Negative Exponents DEFINITION OF NEGATIVE EXPONENTS a -n is the reciprocal of a n . , where a is not equal to 0.

13. Example What this really means is that you turn a negative exponent into a positive exponent by shifting the power from numerator to denominator or vice versa ! Important – only move the base number and the negative exponent that goes with it!

14. NUMBERS WITH NEGATIVE EXPONENTS FOLLOW THE SAME LAWS OF EXPONENTS

15. The Laws of Exponents: #2: Multiplicative Law of Exponents: If the bases are the same And if the operations between the bases is multiplication, then the result is the base powered by the sum of individual exponents .

16. The Laws of Exponents: #3: Division Law of Exponents: If the bases are the same And if the operations between the bases is division, then the result is the base powered by the difference of individual exponents .

17. The Laws of Exponents: #4: Exponential Law of Exponents: If the exponential form is powered by another exponent, then the result is the base powered by the product of individual exponents.

18. The Laws of Exponents: #5: Product Law of Exponents: If the product of the bases is powered by the same exponent, then the result is a multiplication of individual factors of the product, each powered by the given exponent.

19. The Laws of Exponents: #6: Quotient Law of Exponents: If the quotient of the bases is powered by the same exponent, then the result is both numerator and denominator , each powered by the given exponent.

20. The Laws of Exponents: #7: Negative Law of Exponents: If the base is powered by the negative exponent, then the base becomes reciprocal with the positive exponent.

21. The Laws of Exponents: #8: Zero Law of Exponents: Any base powered by zero exponent equals one 112 = 1 a = 1

22. USE OF EXPONENTS TO EXPRESS SMALL NUMBERS IN STANDARD NUMBER

23. THE DISTANCE FROM EARTH TO SUN IS 149,600,000,000 m = 1.496 X 10 11 THE SPEED OF LIGHT IS 300,000,000m/sec = 3 X 10 11 THE AVERAGE DIAMETER OF A RED BLOOD CELL IS 0.000007 mm = 7 X 10 6 THE DISTANCE OF MOON FROM THE EARTH IS 384,467,000m = 3.84467 X 10 8 AVERAGE RADIUS OF THE SUN IS 69,55,000 km= 6.955 X 10 6

24. COMPARING VERY LARGE AND VERY SMALL NUMBERS

25. The diameter of the Sun is 1.4 X 10 9 m and the diameter of the Earth is 1.2756 X 10 7 m . Suppose you want to compare the diameter , with the diameter of the Sun. Diameter of the Sun = 1.4 X 10 9 m Diameter of the Earth = 1.27556 X 10 7 m Therefore 1.4 X 10 9 1.27556 X 10 7 = 1.4 X 10 9-7 1.2756 = 1.4 X 100 1.2756 Which is approximately 100 times the diameter of the earth .

26. MULTIPLE CHOICE QUESTIONS (i) ( a/b) m ab m a m / b m (ii) 5 -1 X 3 is 3/5 5/3 (iii) The value of 1 a X m a 1 m a (iv) The standard form of 1.870000 is 1.87 X 10 5 1.87 X 10 6

27. (v) 13 5 ÷ 169 is equal to 13 7 13 3 (vi) The reciprocal of (3 2 ) 4 3 8 1 / 3 8 (vii) Compare 5 X 10 7 ; 6 X 10 4 (a) 5 X 10 7 is greater (b) 6 X 10 4 is greater Find the value of 3 4 X 9 3 6 3 4

28. Find the value of n : X [ a 8 ] = (a n-6 ) Solution : = a 5-3 x a 8 = a n-6 [ a m ÷ a n = a m-n ] = a 2 x a 8 = a n-6 = a 10 = a n-6 = a 10 + 6 Ans. n = 16  

29. Q.2 Find the value of X Solution : ( =( 3+5 = 2x +1 = 8 = 2x +1 = 8-1 = 2x = 7 = 2x A ns . = x  

30. THANK YOU !