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Potenciação

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Potenciação

  1. 1. POTENCIAÇÃO
  2. 2. O QUE SÃO AS POTÊNCIAS: As potências surgiram no intuito de representar multiplicações onde os fatores eram iguais.Exemplo:3x3x3x3 é o 3 vezes ele mesmo 4 vezesMultiplicação comFatores iguais
  3. 3. Representamos uma potência da seguinte forma: base expoente 3 4 =3 x 3 x 3 x 3 = 81Chamamos de: base sempre valor do fator ;expoente é a quantidade de vezes que o fator semultiplica;potência é o resultado do produto.
  4. 4. Casos especiais: EXPOENTES:1: Toda potenciação cujo expoente é 1 tem como resultado o valor da base.Exemplo: 71 = 70 : Toda potenciação cujo expoente é zero o resultado será sempre 1.Exemplo: 120 = 1
  5. 5. Base:10: Para calcular uma potenciação com base igual a dez basta escrever zeros igual ao número do expoente.Exemplo: 108 = 100.000.000 (8 zeros)Ou seja105 = 100.000 5 zeros
  6. 6. Multiplicação entre Bases IguaisA Regra é: Repete a Base e SOMA os Expoentes.Exemplos : 22 . 23 = 2 2 + 3 = 25 = 2 x 2 x 2 x 2 x 2 = 32 51 . 53 = 5 1 + 3 = 54 = 5 x 5 x 5 x 5 = 625
  7. 7. Divisão entre Bases IguaisA Regra é:Repete a Base e SUBTRAI os Expoentes.Exemplos : 28 ÷ 23 = 2 8- 3 = 25 = 2 x 2 x 2 x 2 x 2 = 32 57 . 53 = 5 7-3 = 54 = 5 x 5 x 5 x 5 = 625
  8. 8. Potência de PotênciaRegra é: Repete a Base e MULTIPLICA-SE os ExpoentesExemplos:(85)6 = 85x6 = 830(153)9 = 153x9 = 1527
  9. 9. Potência de um ProdutoRegra: DISTRIBUIR a Potência para as BasesExemplos:(14 x 9)5 = 145 x 95(21 x 3)8 = 218 x 38
  10. 10. Expoente Negativo Qualquer número diferente de zero elevado a um expoente negativo é igual ao inverso deste número elevado ao oposto do expoente. −4 4Exemplo:  1 6  3  5 18 −6 =     =    18   5  3 Inverte-se a base e troca o sinal do expoente.
  11. 11. BASE NEGATIVAFazer o cálculo numérico normalmente e verificar se o valor do expoente é :- PAR: Resultado será POSITIVO- ÍMPAR: Resultado será NEGATIVO- Exemplo:(-15)2 = 225 (-7)3 = -373
  12. 12. BASE FRACIONÁRIAQuando a base de uma potenciação for uma fração é necessário calcular a potenciação tanto para o numerador quanto para o numerador.Aplica-se a regra de DISTRIBUTIVA!Exemplo: 3 3  7 7 343   = 3 =  5 5 125
  13. 13. Atividades:Use as propriedades de potencias nas expressões. a) 73 . 75 b) 53 . 54 . 52 c) 105 : 105 d) 45 : 43 e) (52)5 [(56)0]8 (7 . 10)3 ( 2 . 32 . 52)4
  14. 14. 3 - Reduza a uma só potencia:a) (-3)⁵ . (-3)² b) (-8) . (-8) . (-8)c) (-5)³ . (-5) . (-5)² d) (-3)⁷ : (-3)²e) (-4)² : (-4)² f) [(-4)² ]³g) [(-3)³ ]² h) [(-5)⁰ ]³

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