Indices

The English mathematician Augustus de Morgan has given his age in algebraic terms. Can you work out when he was born?

How much money did the Queen give away in pence as a power of 2?

What does this number mean ? Which order of 1, 2, 3 and 4 makes the highest value ? Which makes the lowest ?

When is $7^n + 3^n$ a multiple of 10? Can you prove the result by two different methods?

Add powers of 3 and powers of 7 and get multiples of 11.

Which of these five algebraic expressions is largest, given $x$ is between 0 and 1?

How many zeros are there at the end of $3^4 \times 4^5 \times 5^6$?

The sums of the squares of three related numbers is also a perfect square - can you explain why?

Find 180 to the power 59 (mod 391) to crack the code. To find the secret number with a calculator we work with small numbers like 59 and 391 but very big numbers are used in the real world for this.