Powers and roots

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

From this sum of powers, can you find the sum of the indices?

What are the last two digits of 2^(2^2003)?

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?

Is it true that $99^n$ has 2n digits and $999^n$ has 3n digits? Investigate!

Investigate $1^n + 19^n + 20^n + 51^n + 57^n + 80^n + 82^n $ and $2^n + 12^n + 31^n + 40^n + 69^n + 71^n + 85^n$ for different values of n.

The problem is how did Archimedes calculate the lengths of the sides of the polygons which needed him to be able to calculate square roots?

However did we manage before calculators? Is there an efficient way to do a square root if you have to do the work yourself?

What is the least square number which commences with six two's?

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