Competition problem — Algebra — Maths Olympiad Prep

Library / /16 of 173

Algebra Difficulty 1.9 Junior Find the answer

If $10^n = 1000^{20}$ , what is the value of $n$ ?

Your answer

A number or a short expression. Spacing and $ signs are ignored.

Solution

Using exponent laws, $1000^{20}=\left(10^{3}\right)^{20}=10^{60}$ and so $n=60$ .

Want a route through all this instead of an archive? The track puts 2,000 problems in a working order, from AMC 10 level to the IMO shortlist.

Source: Omni-MATH, licensed Apache-2.0. Statement and solution reproduced as published; topic and difficulty added by this site.