Mind Map Gallery Exponents and Powers
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Math Project - Exponents and Powers: Laws of Exponents Expanding Numbers To Write Larger Numbers in a Shorter Form
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