4. Calcule o valor de cada uma das expressões: a) 0,2^2 b) 0,05^-2 C) ((2^4)^3cdot 2^7cdot 2^3)/((2^11))^(2) 1) A=((3)/(4))^2cdot (-2)^3+(-(1)/(2))^1 e) Sendoa=(2^48+4^22-2^46)/(4^3)cdot 8^(6) - valor de (1)/(26)cdot a

Vamos calcular o valor de cada uma das expressões:<br /><br />a) \(0,2^{2}\)<br />\[0,2^{2} = 0,04\]<br /><br />b) \(0,05^{-2}\)<br />\[0,05^{-2} = \left(\frac{1}{0,05}\right)^{2} = 20^{2} = 400\]<br /><br />c) \(\frac{(2^{4})^{3} \cdot 2^{7} \cdot 2^{3}}{(2^{11})^{2}}\)<br />\[= \frac{2^{12} \cdot 2^{7} \cdot 2^{3}}{2^{22}} = \frac{2^{22}}{2^{22}} = 1\]<br /><br />d) \(A = \left(\frac{3}{4}\right)^{2} \cdot (-2)^{3} + \left(-\frac{1}{2}\right)^{1}\)<br />\[= \left(\frac{9}{16}\right) \cdot (-8) + \left(-\frac{1}{2}\right) = -\frac{72}{16} - \frac{1}{2} = -4.5\]<br /><br />e) \(Sendo a = \frac{2^{48} + 4^{22} - 2^{46}}{4^{3} \cdot 8^{6}}\)<br />\[a = \frac{2^{48} + (2^{2})^{22} - 2^{46}}{(2^{2})^{3} \cdot (2^{3})^{6}} = \frac{2^{48} + 2^{44} - 2^{46}}{2^{6} \cdot 2^{18}} = \frac{2^{48} + 2^{44} - 2^{46}}{2^{24}} = \frac{2^{24}(2^{24} + 2^{20} - 2^{22})}{2^{24}} = 2^{24} + 2^{20} - 2^{22} = 2^{22}(2^{2} + 2^{4} - 2^{2}) = 2^{22}(4 + 16 - 4) = 2^{22} \cdot 16 = 2^{22} \cdot 2^{4} = 2^{26} = 64 \cdot 2^{24} = 64 \cdot 16777216 = 1073741824\]<br />\[\frac{1}{26} \cdot a = \frac{1073741824}{26} = 41207000\]<br /><br />Portanto, os valores das expressões são:<br />a) 0,04<br />b) 400<br />c) 1<br />d) -4.5<br />e) 41207000