90.1.4 Rational Number Part 1.4 Indix and power (Part 1)

90.1.4 Rational Number Part 1.4 Indix and power (Part 1)

Power and Exponents

Mind it

A. 

★    a = 1a

★    a + a = 2a

★    a + a + a = 3a

★    a + a + a + a = 4a

★   3a =  a + a + a 

★   2a =  a + a 

★   1a =  a

 B. 

★   a⁰ = 1

★   a¹ = a

★   a² = a × a

★   a³ = a × a × a

★   a⁵ = a × a × a × a × a

★   a × a × a × a × a = a⁵

★   a × a × a × a = a⁴

★   a × a × a = a³

★   a × a = a²

★ a⁰        = 1

★ a^m × aⁿ  = (a)^m+n

★ a^l × a^m × aⁿ  = (a)^{l + m +n}

★ (a^m) ⁿ = a^m×n

★ a^m × b^m  = (ab)^m

★ a^m  ÷ aⁿ  = (a)^{m –n}

★ a^m  ÷ b^m  = (a/b)^m

a) Converting the positive exponent into negative:

(i)

               1

a^m  =    _____

               a^–m

(ii)

(a/b)^m = (b/a)^–m     

b) Converting the negative exponent into posative:

(i)

                   1

a^–m  =     ______

                  a^m

(ii)

(a/b)^–m = (b/a)^m     

Identity 1

(a + b) (a + b) 

(a + b)² = a² + b² + 2ab 

                  Or

a² + b² + 2ab = (a + b)²

Identity 2

(a – b) (a – b) 

(a – b)² = a² + b^{2 –} 2ab 

                  Or

a² + b^{2 –} 2ab = (a – b)²

Identity 3

(a +b)(a –b)  = a² – b²  

                  Or

a² – b²  = (a +b)(a –b)

Identity 1

r₁²

01. Write the followings in exponential from:

(01) 2 × 2 

(02) 2 × 2 × 2 × 2

(03) 2 × 2 × 2 × 2 × 2 × 2

(04) 3 × 3 × 3 × 3 × 3 × 3 × 3

(05) 5 × 5

(06) (3/2) × (3/2) × (3/2)

(07) (1/2) × (1/2) × (1/2) × (1/2)

(08) (3/2) × (3/2) × (3/2) × (3/2) × (3/2)

(09) (5/7) × (5/7) × (5/7)

(10) (1/3) × (1/3) × (1/3) × (1/3) × (1/3) × (1/3) × (1/3)

02. Write the following into the factorial from:

(01) 2⁵

(02) 5²

(03) 3⁴

(04) 9³

(05) 5⁴

(06) (3/2)³

(07) (1/2)⁴

(08) (3/2)⁵

(09) (5/7)³

(10) (1/3)⁷

03. Find the value of the followings:

(01) 2⁵

(02) 5²

(03) 3⁴

(04) 9³

(05) 5⁴

(06) (3/2)³

(07) (1/2)⁴

(08) (3/2)⁴

(09) (5/7)³

(10) (1/3)⁷

04. Write the followings in exponential from:

(01) 4 

(02) 16

(03) 64

(04) 729

(05) 343

(06) (27/8)

(07) (1/16)

(08) (243/32)

(09) (125/343)

(10) (1/2187)

05. Convert the following into the negative exponent:

(01) 2⁵

(02) 5²

(03) 3⁴

(04) 9³

(05) 5⁴

(06) (3/2)³

(07) (1/2)⁴

(08) (3/2)⁵

(09) (5/7)³

(10) (1/3)⁷

06. Convert the following into the posative exponent:

(01) 2^–5

(02) 5^–2

(03) 3^–4

(04) 9^–3

(05) 5^–4

(06) (3/2)^–3

(07) (1/2)^–4

(08) (3/2)^–5

(09) (5/7)^–3

(10) (1/3)^–7

07. Find the value of the followings:

(01) (a²)²

(02) (2²)³

(03) (5²)³

(04) (3²)⁵

(05) (3²)³

(06) (4²)^½

(07) (2²)^¼

(08) (5³)^⅓

(09) (3⁵)^⅕

(10) (7⁷)^⅐

(11) (–x²)⁰

(12) (2²)³

(13) (5^1/3)³

(14) (7^1/2)⁰

(15) (3^1/5)⁵

08. Right the given expression into simplest form:

(01) (81)^1/2

(02) (16)^3/4

(03) (32)^1/5

(04) (125)^1/3

(05) (16)^1/4

(06) (64)^1/2

(07) (4)^1/2

(08) (216)^2/3

(09) (256)^3/4

(10) (125)^–1/3

(12) (32)^2/5

(12) (1000)^2/3

(13) (9)^3/2

(14) (27)^1/3

(15) (81)^1/4

(16) (2187)^1/7