# 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

Laws of Exponents

Expanding Numbers

To Write Larger Numbers in a Shorter Form

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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

Powers of Same Base

a ᵐ / a ⁿ = a ᵐ ⁻ ⁿ

2 ⁷ / 2 ⁵ = 2 ⁷ ⁻ ⁵ = 2

Powers with Same Exponent

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