Multiplying Fractions · Superchallenge problem

A copy machine is set to shrink: every copy it makes is $\dfrac{3}{4}$ as long and $\dfrac{3}{4}$ as wide as the page it copies. Zoe draws a line $16$ cm long. She copies her drawing, then copies the copy, then copies that copy, and so on. How many copies does she have to make before the line is shorter than $5$ cm for the first time?