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Big Powers

Three people chose this as a favourite problem. It is the sort of problem that needs thinking time - but once the connection is made it gives access to many similar ideas.

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Powerful Zeros

Weekly Problem 32 - 2006
How many zeros are there at the end of $3^4 \times 4^5 \times 5^6$?

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Largest Expression

Weekly Problem 36 - 2006
Which of these five algebraic expressions is largest, given $x$ is between 0 and 1?

Stars in the Sky

Stage: 4 Short Challenge Level: Challenge Level:1

According to one astronomer, there are one hundred thousand million galaxies in the universe, each containing one hundred thousand million stars. As a power of $10$, how many stars is that altogether?

If you liked this problem, here is an NRICH task that challenges you to use similar mathematical ideas.

This problem is taken from the UKMT Mathematical Challenges.
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