Write the rational number 5.3¹3¹3¹3¹... as the ratio of two integers

1 answer

5.3¹3¹3¹3¹... = 5.3⁰ × 3⁴⁰ = 5,764,801,558,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,945,