1. Resolver as potências: **a)** $(\frac{1}{6})^2 = \frac{1^2}{6^2} = \frac{1}{36}$ **b)** $(\frac{3}{4})^0 = 1$ (qualquer número diferente de zero elevado a zero é 1) **c)** $(\frac{2}{3})^{-1} = \frac{1}{(\frac{2}{3})} = \frac{3}{2}$ **d)** $2^3 = 2 \times 2 \times 2 = 8$ **e)** $148^1 = 148$ **f)** $3^5 \times 3^2 = 3^{5+2} = 3^7 = 2187$ **g)** $5^{-3} = \frac{1}{5^3} = \frac{1}{125}$ **h)** $7^1 = 7$ **i)** $\sqrt{\frac{225}{256}} = \frac{\sqrt{225}}{\sqrt{256}} = \frac{15}{16}$ **j)** $\sqrt{\frac{256}{256}} = \frac{\sqrt{256}}{\sqrt{256}} = \frac{16}{16} = 1$ **k)** $-\sqrt{\frac{64}{49}} = -\frac{\sqrt{64}}{\sqrt{49}} = -\frac{8}{7}$ 2. Resolver os cálculos e simplificar: **a)** $\frac{2}{5} + \frac{3}{5} = \frac{2+3}{5} = \frac{5}{5} = 1$ **b)** $\frac{2}{10} + \frac{3}{5} = \frac{2}{10} + \frac{6}{10} = \frac{2+6}{10} = \frac{8}{10} = \frac{4}{5}$ **c)** $\frac{9}{5} - \frac{2}{5} = \frac{9-2}{5} = \frac{7}{5}$ **d)** $\frac{1}{2} - \frac{2}{6} = \frac{3}{6} - \frac{2}{6} = \frac{1}{6}$ **e)** $\frac{3}{3} \times \frac{4}{7} = 1 \times \frac{4}{7} = \frac{4}{7}$ **f)** $\frac{5}{7} + \frac{2}{3} = \frac{15}{21} + \frac{14}{21} = \frac{29}{21}$ 3. Resolver as equações do 1º grau: **a)** $2x - 13 = 3 + 6x$ Passo 1: $2x - 13 = 3 + 6x$ Passo 2: $2x - 6x = 3 + 13$ Passo 3: $\cancel{2x} - 6x = 16$ Passo 4: $-4x = 16$ Passo 5: $x = \frac{16}{-4} = -4$ **b)** $2(x + 3) + 3(x + 2) = x + 3(2x - 12)$ Passo 1: $2x + 6 + 3x + 6 = x + 6x - 36$ Passo 2: $5x + 12 = 7x - 36$ Passo 3: $5x - 7x = -36 - 12$ Passo 4: $\cancel{5x} - 7x = -48$ Passo 5: $-2x = -48$ Passo 6: $x = \frac{-48}{-2} = 24$ **c)** $\frac{2}{6} + \frac{x}{3} - 3 = 0.5$ Passo 1: $\frac{1}{3} + \frac{x}{3} - 3 = 0.5$ Passo 2: $\frac{1+x}{3} - 3 = 0.5$ Passo 3: $\frac{1+x}{3} = 3.5$ Passo 4: $1 + x = 3.5 \times 3 = 10.5$ Passo 5: $x = 10.5 - 1 = 9.5$ 4. Calcular na equação $y = 5x + 6$: **a)** Para $x = -5$, $y = 5(-5) + 6 = -25 + 6 = -19$ **b)** Para $x = 2$, $y = 5(2) + 6 = 10 + 6 = 16$ **c)** Para $x = -1$, $y = 5(-1) + 6 = -5 + 6 = 1$ 5. Calcular na equação $y = 7x - 3$: **a)** Para $y = -2$, $-2 = 7x - 3$ então $7x = 1$ e $x = \frac{1}{7}$ **c)** Para $y = -\frac{1}{2}$, $-\frac{1}{2} = 7x - 3$ então $7x = \frac{5}{2}$ e $x = \frac{5}{14}$