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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 .

Pergunta

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 .

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 .

Solução

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BernardoElite · Tutor por 8 anos

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<p><br />1.a) (1/2)^-2 + [2^-1 - (-2)^-1]^-1 = 3<br />1.b) (3^1/3)^6 / 4 x 9^1/2 = 3 / 2<br />1.c) 0.000001 x (0.01)^2 x 10000 / 0.0001 = 10<br />1.d) (2^-1 + 2^-1/2)^-2 = 25 / 36<br />1.e) 3Root(2^28 + 2^30 ) / 10 = 6 x 2^8 = 1536.<br />2) For expression M=(a^3x + {a -3x}) / (a ^ x + a -x}), with a ^ 2x = 3, will be equal to 1<br /> </p>

Explicação

<p> <br />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.<br />Each question will be dealt with respectively as follows:<br />a) It applies the properties of exponents and the idea of inverse numbers, with the particularity of having negative exponents.<br />b) It includes cube and square roots and applies properties of exponents such as distributive.<br />c) It involves multiplication and division combined with scientific notation usage.<br />d) Utilize properties of equivalence between fraction division and exponentiation, multiply both terms and take square Roots for -2. <br />e) After applying the cube root and reducing same basis exponent with different degrees, the expression can simplify all orders.<br />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.<br /><br /></p>
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