Powers and roots

What can you say about the values of n that make $7^n + 3^n$ a multiple of 10? Are there other pairs of integers between 1 and 10 which have similar properties?

What is the last digit of the number 1 / 5^903 ?

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

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

Can you show that 1^99 + 2^99 + 3^99 + 4^99 + 5^99 is divisible by 5?

Find the five distinct digits N, R, I, C and H in the following nomogram

Can you work out the value of x in this 'power-full' equation?

A wooden cube with edges of length 12cm is cut into cubes with edges of length 1cm. What is the total length of the all the edges of these centimetre cubes?

What fractions can you find between the square roots of 65 and 67?

The squares of any 8 consecutive numbers can be arranged into two sets of four numbers with the same sum. True of false?