(-2/3)^-3 - (-2)^-2

Passo 1

Beleza, vamos dar uma olhada no que o exercício está pedindo. A gente tem a expressão (-2/3)^-3 - (-2)^-2. A matéria aqui envolve potências com expoentes negativos. Para resolver isso, precisamos saber como trabalhar com expoentes negativos e como simplificar frações elevadas a potências.

Passo 2

Primeiro, vamos lidar com cada termo separadamente. Vamos começar com . Quando temos uma fração elevada a um expoente negativo, a gente inverte a fração e muda o sinal do expoente para positivo. Então:
y = sen(x^2)

Passo 3

Agora, vamos calcular . Lembra que elevar uma fração a um expoente significa elevar o numerador e o denominador separadamente. Além disso, como o expoente é ímpar, o sinal negativo fica:
y = sen(x^2)

Passo 4

Vamos para o segundo termo: . Assim como antes, um expoente negativo significa que a gente inverte a base e torna o expoente positivo:
y = sen(x^2)

Passo 5

Agora, calculamos . Como o expoente é par, o resultado será positivo:
y = sen(x^2)
Então:
y = sen(x^2)

Passo 6

Agora que temos os dois termos simplificados, vamos substituí-los de volta na expressão original:
y = sen(x^2)

Passo 7

Para subtrair essas frações, precisamos de denominadores iguais. O mínimo múltiplo comum entre 8 e 4 é 8. Então, vamos ajustar a segunda fração:
y = sen(x^2)

Passo 8

Agora, podemos somar os numeradores:
y = sen(x^2)

Resposta

A expressão (-2/3)^-3 - (-2)^-2 é igual a .

Exercícios relacionados

-raiz(8) + 16^(1/4) - (-2) + 27^(1/3)
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Esboce o gráfico de uma função que seja contínua exceto para a descontinuidade declarada.
c) Descontinuidade removivel em 3 .