Question

Como resolve?? [((2 ^ 2) ^ 2 + 3 ^ 2)/(2 ^ 2 * 3 ^ 2)] ^ (1/2)

Answer 1

Observe com atenção:

$\bigg(\dfrac{(2^2)^2+3^2}{2^2\cdot3^2}\bigg)^\frac{1}{2}=$

$=\bigg(\dfrac{2^{2\cdot2}+3^2}{2^2\cdot3^2}\bigg)^\frac{1}{2}=$

$=\bigg(\dfrac{2^4+3^2}{2^2\cdot3^2}\bigg)^\frac{1}{2}=$

$=\bigg(\dfrac{2\cdot2\cdot2\cdot2+3\cdot3}{2\cdot2\cdot3\cdot3}\bigg)^\frac{1}{2}=$

$=\bigg(\dfrac{16+9}{4\cdot9}\bigg)^\frac{1}{2}=$

$=\bigg(\dfrac{25}{36}\bigg)^\frac{1}{2}=$

$=\sqrt[2]{\bigg(\dfrac{25}{36}\bigg)^1}=$

$=\sqrt[2]{\dfrac{25}{36}}=$

$=\dfrac{\sqrt[2]{25}}{\sqrt[2]{36}}=$

$=\dfrac{\sqrt[2]{5^2}}{\sqrt[2]{6^2}}=$

$=\underline{\boxed{\dfrac{5}{6}}}\,.$