MindMap Gallery Exponents and Powers
Math Project - Exponents and Powers: Laws of Exponents Expanding Numbers To Write Larger Numbers in a Shorter Form
Middle School Math Concepts
Comparing And Contrasting Linear Functions and Quadratic Functions
SAT Math Khan Academy Tutorials and Exercises
Maths Study
Coordinate Geometry Concept Map
Further Transcendental Function
Number System
Partial Derivatives Higher Order
Matrices
Calculus Mind Map
Exponents and Powers
Laws of Exponents
(-1) odd numbers = -1(-1) odd numbers = 1
A & B are non zero integersM & N are whole numbers
Powers of Same Base
a ᵐ x a ⁿ = a ᵐ ⁺ ⁿ
E.g:- 2 ² x 2 ³ = 2 ² ⁺ ³
Powers with Same Exponent
a ᵐ x b ᵐ = (ab) ᵐ
E.g: 2 ³ x 3 ³ = (2x3) ³ = 6 ³
a ᵐ / a ⁿ = a ᵐ ⁻ ⁿ
2 ⁷ / 2 ⁵ = 2 ⁷ ⁻ ⁵ = 2
a ᵐ / b ᵐ = (a/b) ᵐ
3 ⁴ x 5 ⁴ = (3 / 5) ⁴
Power of Power
(a ᵐ) ⁿ = a ᵐ ˣ ⁿ
(2 ³) ² = 2 ³ ˣ ² = 2 ⁶ = 64
Numbers with Exponent Zero
a ᵐ / a ᵐ = 1a ᵐ ⁻ ᵐ = a ⁰ = 1a ⁰ = 1
26 ⁰ = 1Any base to the power 0 is 1
Expanding Numbers
4756 = 4 x 1000 + 7 x 100 + 5 x 10 + 6 = 4 x 10 ³ + 7 x 10 ² + 5 x 10 ¹ + 6 x 10 ⁰
Larger Numbers in Standard Forms
Diameter of Earth: 1, 27, 56, 000 = 1.2756 x 10 ⁷
Distance between Earth and the Moon: 38 ,40 ,00 ,000 = 3.84 x 10 ⁸
Speed of Light in vacuum = 300000000 = 3 x 10 ⁸
To Write Larger Numbers in a Shorter Form
a ² = a x a
( a square )
a ³ = a x a x a
( a cube )
10, 000 = 10 x 10 x 10 10 = 10 ⁴
Read as 10 raised to the power 4or 4 power of 10
4 - exponent
10 base
As Products of Prime Numbers
1000 = 500 x 2
1000 = 2 x 2 x 250
1000 = 2 x 2 x 2 x 125
1000 = 2 x 2 x 2 x 5 x 25
1000 = 2 x 2 x 2 x 5 x 5 x 5
1000 = 2 ³ x 5 ³
432 = 2 x 216
432 = 2 x 2 x 108
432 = 2 x 2 x 2 x 54
432 = 2 x 2 x 2 x 2 x 3 x 9
432 = 2 x 2 x 2 x 2 x 3 x 3 x 3
432 = 2 ⁴ x 5 ³