Exponents and Powers

Exponents and PowersLaws of ExponentsExpanding Numbers(-1) odd numbers = -1(-1) odd numbers = 1A & B are non zero integersM & N are whole numbersPowers of Same Basea ᵐ x a ⁿ = a ᵐ ⁺ ⁿPowers with Same ExponentPowers of Same BasePowers with Same ExponentPower of PowerNumbers with Exponent ZeroE.g:- 2 ² x 2 ³ = 2 ² ⁺ ³a ᵐ x b ᵐ = (ab) ᵐE.g: 2 ³ x 3 ³ = (2x3) ³ = 6 ³a ᵐ / a ⁿ = a ᵐ ⁻ ⁿ2 ⁷ / 2 ⁵ = 2 ⁷ ⁻ ⁵ = 2 a ᵐ / b ᵐ = (a/b) ᵐ3 ⁴ x 5 ⁴ = (3 / 5) ⁴ (a ᵐ) ⁿ = a ᵐ ˣ ⁿ(2 ³) ² = 2 ³ ˣ ² = 2 ⁶ = 64a ᵐ / a ᵐ = 1a ᵐ ⁻ ᵐ = a ⁰ = 1a ⁰ = 1 26 ⁰ = 1Any base to the power 0 is 14756 = 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 ⁰To Write Larger Numbers in a Shorter Forma ² = a x aa ³ = a x a x aLarger Numbers in Standard FormsDiameter of Earth: 1, 27, 56, 000 = 1.2756 x 10 ⁷Distance between Earth and the Moon: 38 ,40 ,00 ,000 = 3.84 x 10 ⁸Speed of Light in vacuum = 300000000 = 3 x 10 ⁸( a square )( a cube )10, 000 = 10 x 10 x 10 x 10 = 10 ⁴Read as 10 raised to the power 4or 4 power of 104 - exponent10 baseAs Products of Prime Numbers1000 = 500 x 2432 = 2 x 2161000 = 2 x 2 x 250 1000 = 2 x 2 x 2 x 1251000 = 2 x 2 x 2 x 5 x 251000 = 2 x 2 x 2 x 5 x 5 x 51000 = 2 ³ x 5 ³432 = 2 x 2 x 108432 = 2 x 2 x 2 x 54432 = 2 x 2 x 2 x 2 x 3 x 9432 = 2 x 2 x 2 x 2 x 3 x 3 x 3432 = 2 ⁴ x 5 ³
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