 # Exponents and Division

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Exponents and Division
OUR LESSON: Exponents and Division Confidential

Warm Up (a3.b4.c0) . (a6.b2) = a9b6 (-2a2b4)2 . -3a3 = -12a7b8
7ba2 . 3ab = 21a3b2 6a . 2a = 12a2 (2k) (5k3)2 = 50k7 Confidential

Large numbers can be represented by scientific notations
Revision Large numbers can be represented by scientific notations 2 x 103 = 2000 So we know that 10 to the power of 3 is 10 x 10 x 10 = 1000 And 2 x 1000 = 2000 Confidential

26 Exponent or Power Base Here 2 is the Base and 6 is the Power of 2
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Any number to the power 0 is equal to 1
26 = 2 x 2 x 2 x 2 x 2 x 2 and 20 = 1 Any number to the power 0 is equal to 1 Confidential

Laws of multiplying Bases
Rule for multiplying bases am x an = a m + n Product to a power (zy)n = z n x y n Power to a Power (am)n = a m x n Confidential

Lets see some examples (10ab)0 = 1 (-7xy)2 = 49x2y2
(-4)2 . (-4)3 = (-4)5 = -1024 (23ab)2 . a3 = 26 a2+3 b2 = 64 a5b2 Confidential

1. Quotient Law cm ÷ cn = c m - n 2. Power of a quotient law
Lets get started Laws of Dividing Bases 1. Quotient Law cm ÷ cn = c m - n 2. Power of a quotient law (z / y)n = z n / y n Confidential

4.Power to a Power (am / bm)n = amn / bmn Laws of Dividing Bases
3. Negative Exponents X -1 = 1 / X 4.Power to a Power (am / bm)n = amn / bmn Confidential

cm ÷ cn = cm - n Quotient Law
Division of one power by another power If c is any non-zero number and m is a larger number than n, m>n, we can write cm ÷ cn = cm - n Confidential

Base (c) is same, we only subtract the exponents
In symbols if c is any non-zero number, but if n > m, we get Base (c) is same, we only subtract the exponents 1 cm ÷ cn = cm-n = c n - m Confidential

Lets get it better with an Example of each type
25 ÷ 23 = 2 x 2 x 2 x 2 x 2 = 25-3 = 22 2 x 2 x2 n < m = 2 x 2 = 4 62 ÷ 65 = x 6 1 = 6 x 6 x 6 x 6 x 6 6 x 6 x 6 n > m 1 1 = 1 or = 65-2 63 216 Confidential

In this we raise a quotient or fraction to a power
Power of a quotient law Dividing with the same exponents In this we raise a quotient or fraction to a power If z is any number, and y is any non-zero number, then Here the power (n) is same so we multiply the z/y fraction ‘n’ number of times n n z z = = n y y Confidential

Lets understand this concept with an example
3 3 3 27 3 x x = = = 4 4 3 64 Confidential

Negative Exponent Negative Exponent It indicates the reciprocal of base as a fraction (not a negative number) It indicates the reciprocal of base as a fraction (not a negative number) 1 1 1 1 -m m X = X = X = X = x x m x x -m Confidential

2 (-5) Lets try an example 1 1 23 8 = = -2 1 1 = = (-5) x (-5) 25 -3
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is not allowed Remember Anything to the power of zero is equal to 1
is not allowed Anything to the power of zero is equal to 1 For example (-7)0 = 1 1 30 = 1 = 1 30 Confidential

42 . 3 63 . 3 Power to a Power 42 46 69 63 (am / bm)n = amn / bmn 3
For Example: 3 42 42 . 3 46 256 = = = 69 63 63 . 3 432 Confidential

c am x an = a m + n 1 cm ÷ cn = (am / bm)n = a mn / b mn Remember
When the base is same, we add /subtract the powers (exponents) as required am x an = a m + n When the bases are different, we multiply the powers 1 cm ÷ cn = c m - n (am / bm)n = a mn / b mn Confidential

Your turn! 56/ = = 1/25 58/ 56 = = 25 25/ 23 = = 4 (3/5)2 = 32/52 = 9/25 = 1/72 = 1/49 Confidential

Questions 6. [42/33]2 = 44/36 = 256/729 7. (-3)-3 = 1 /-27 90/80 = 1
6. [42/33]2 = 44/36 = 256/729 7. (-3) = 1 /-27 90/ = 1 72/ = 49/36 [5/7]3 = 125/343 Confidential

Break time Confidential

Confidential

1. (2 x 3)4 (24) (34) = (32) (25) (32) (25) = 24-5 x 34-2 = 2-1 x 32 =
9/2 Confidential

2. Arrange from greatest to least
2-5, 5-2, 33 , (-4)-3 , (-3)-4 , 2-5 = 1/32 5-2 = 1/25 33 = 27 (-4)-3= 1/64 (-3)-4 = 1/81 27, 1/25, 1/32, 1/64, 1/81 Confidential

3. 3m-3 42 12 m-3-(-2) n-6 = 4m-2 n-6 = 12m-1n-6 Confidential

1. Quotient Law cm ÷ cn = c m - n 2. Power of a quotient law
Lets review what we have learned today Laws of Dividing Bases 1. Quotient Law cm ÷ cn = c m - n 2. Power of a quotient law (z / y)n = z n / y n Confidential

4.Power to a Power (am / bm)n = amn / bmn Laws of Dividing Bases
3. Negative Exponents X -1 = 1 / X 4.Power to a Power (am / bm)n = amn / bmn Confidential

cm ÷ cn = cm ÷ cn = cm - n c 1 Quotient Law n - m
If c is any non-zero number and m is a larger number than n, m > n, we can write cm ÷ cn = cm - n In symbols if c is any non-zero number, but if n > m, we get 1 cm ÷ cn = c n - m Confidential

In this we raise a quotient or fraction to a power
Power of a quotient law Dividing with the same exponents In this we raise a quotient or fraction to a power Here the power (n) is same so we multiply the z/y fraction ‘n’ number of times n n z z = n y y Confidential

Negative Exponent It indicates the reciprocal of base as a fraction (not a negative number) 1 1 X -m = X m = x m x -m Confidential

00 Power to a Power is not allowed (am / bm)n = amn / bmn
Anything to the power of zero is equal to 1 Confidential

Remember to practice what you have learned!
Great Job done! Remember to practice what you have learned! Confidential