Question
Questão - 1. Calcule o valor das expressões: (a) ((1)/(2))^(-2)+[2^(-1)-(-2)^(-1)]^(-1) (b) (3^(1//3))^(6//4)*9^(1//2) . (c) (0,000001*(0,01)^(2)*10000)/(0,0001) (d) (2^(-1)+2^(-(1)/(2)))^(-2) (e) root(3)((2^(29)+2^(30))/(10)) Questão - 2. Calcule o valor da expressão M=(a^(3x)+a^(-3x))/(a^(x)+a^(-x))". " sendo a^(2x)=3 .
Solution
4.1
(247 Votos)
Bernardo
Elite · Tutor por 8 anos
Resposta
1.a) (1/2)^-2 + [2^-1 - (-2)^-1]^-1 = 31.b) (3^1/3)^6 / 4 x 9^1/2 = 3 / 21.c) 0.000001 x (0.01)^2 x 10000 / 0.0001 = 101.d) (2^-1 + 2^-1/2)^-2 = 25 / 361.e) 3Root(2^28 + 2^30 ) / 10 = 6 x 2^8 = 1536.2) For expression M=(a^3x + {a -3x}) / (a ^ x + a -x}), with a ^ 2x = 3, will be equal to 1
Explicação
This set of questions is related to Mathematics, more specifically the topic of exponents and roots. Exponent elevates a number to the power indicated next to it and roots calculate the power that raises a given number to a certain capacity.Each question will be dealt with respectively as follows:a) It applies the properties of exponents and the idea of inverse numbers, with the particularity of having negative exponents.b) It includes cube and square roots and applies properties of exponents such as distributive.c) It involves multiplication and division combined with scientific notation usage.d) Utilize properties of equivalence between fraction division and exponentiation, multiply both terms and take square Roots for -2. e) After applying the cube root and reducing same basis exponent with different degrees, the expression can simplify all orders.In question 2, the value can be calculated by factoring both the numerator and the denominator and relationship between a & b, to get total 'M' as answer.