# Powers and Roots - Short Problems

### Tenth Power

##### Stage: 3 Short Challenge Level:

Weekly Problem 48 - 2011
Do these powers look odd...

### Rooted Via 10

##### Stage: 3 Short Challenge Level:

Weekly Problem 22 - 2013
How many of the numnbers shown are greater than 10?

### Weekly Problem 6 - 2008

##### Stage: 3 and 4 Challenge Level:

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

### Maundy Money

##### Stage: 3 Short Challenge Level:

Weekly Problem 22 - 2009
How much money did the Queen give away in pence as a power of 2?

### Weekly Problem 47 - 2009

##### Stage: 2 and 3 Short Challenge Level:

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

### Factorised Factorial

##### Stage: 3 Short Challenge Level:

Weekly Problem 17 - 2010
The value of the factorial $n!$ is written in a different way. Can you work what $n$ must be?

### Equal Length Powers

##### Stage: 3 Short Challenge Level:

Weekly Problem 33 - 2010
How many positive integers $n$ exist for which $n^2$ has the same number of digits as $n^3$?

### Powerful Order

##### Stage: 3 and 4 Short Challenge Level:

Weekly Problem 6 - 2011
Powers of numbers might look large, but which of these is the largest...

### No Square Sums

##### Stage: 3 and 4 Short Challenge Level:

Weekly Problem 12 - 2011
How many numbers do you need to remove to avoid making a perfect square?

##### Stage: 3 and 4 Short Challenge Level:

Weekly Problem 13 - 2011
The sum of three square numbers equals $121$. What can those numbers be...

### The Square of My Age

##### Stage: 3 Short Challenge Level:

Weekly Problem 34 - 2011
Lauren and Thomas tell their ages in terms of sums of squares. Can you work out how old they really are?

### Powered Up

##### Stage: 4 Short Challenge Level:

Weekly Problem 38 - 2014
Can you work out the product of these indices?

### Cubic Fractions

##### Stage: 3 and 4 Short Challenge Level:

Weekly Problem 46 - 2014
Which of these powers of fractions has greatest value?

### Mini Cross-number

##### Stage: 3 and 4 Short Challenge Level:

Weekly Problem 47 - 2014
Which digit replaces x in this crossnumber?

### Self-power Squares

##### Stage: 4 Short Challenge Level:

Weekly Problem 15 - 2016
How many integers $n$, between $1$ and $100$ inclusive, have the property that $n^n$ is a square number?

### Doubly Powerful

##### Stage: 3 and 4 Short Challenge Level:

Weekly Problem 38 - 2016
To power should $4^4$ be raised to give $8^8$?

### Powerful Finale

##### Stage: 3 and 4 Short Challenge Level:

Weekly Problem 24 - 2017
What is the last digit of $3^{2011}$?

### Not a Zero

##### Stage: 3 and 4 Short Challenge Level:

Weekly Problem 45 - 2017
What is the last non-zero digit of $2^{57} \times 3^4 \times 5^{53}$?

### Long List

##### Stage: 3 Short Challenge Level:

Weekly Problem 47 - 2017
How many numbers do I need in a list to have two squares, two primes and two cubes?