Question

Calcule o valor da expressão e escreva o resultado na forma de potência de base de 2 18¹/²-8¹/²?

Answer 1

$18^{\,^{1}\!\!\!\diagup\!\!_{2}}-8^{\,^{1}\!\!\!\diagup\!\!_{2}}\\ \\ =\sqrt{18}-\sqrt{8}\\ \\ =\sqrt{3^{2}\cdot 2}-\sqrt{2^{2}\cdot 2}\\ \\ =\sqrt{3^{2}}\cdot \sqrt{2}-\sqrt{2^{2}}\cdot \sqrt{2}\\ \\ =3\sqrt{2}-2\sqrt{2}\\ \\ =\left(3-2 \right )\sqrt{2}\\ \\ =1\sqrt{2}\\ \\ =\sqrt{2}\\ \\ =2^{\,^{1}\!\!\!\diagup\!\!_{2} }\\ \\ \\ \boxed{18^{\,^{1}\!\!\!\diagup\!\!_{2}}-8^{\,^{1}\!\!\!\diagup\!\!_{2}}=2^{\,^{1}\!\!\!\diagup\!\!_{2} }}$