Powers and Roots - Short Problems


This is part of our collection of Short Problems.

You may also be interested in our longer problems on Powers and Roots.

Printable worksheets containing selections of these problems are available here:

Stage 3 ★ Sheet 1 Solutions            Stage 4 ★★ Sheet 1 Solutions
             

Tenth Power

KS 3 Short Challenge Level:

Challenge Level:1

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

Age of Augustus

KS 3 Short Challenge Level:

Challenge Level:1

Weekly Problem 47 - 2009
The English mathematician Augustus de Morgan has given his age in algebraic terms. Can you work out when he was born?

Megabytes and Kilobytes

KS 3 Short Challenge Level:

Challenge Level:1

How many bytes are there in one megabyte?

Square Percentage

KS 3 Short Challenge Level:

Challenge Level:1

Weekly Problem 36 - 2016
What percentage of the integers between 1 and 10,000 are square numbers?

The Square of My Age

KS 3 Short Challenge Level:

Challenge Level:1

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?

Square Triangle

KS 3 Short Challenge Level:

Challenge Level:1

Weekly Problem 42 - 2007
How many triangles have all three angles perfect squares (in degrees)?

Maundy Money

KS 3 Short Challenge Level:

Challenge Level:1

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

Factorised Factorial

KS 3 Short Challenge Level:

Challenge Level:2 Challenge Level:2

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

Powerful Zeros

KS 3 Short Challenge Level:

Challenge Level:2 Challenge Level:2

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

Ordering Fractions

KS 3 & 4 Short Challenge Level:

Challenge Level:1

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

Mini Cross-number

KS 3 & 4 Short Challenge Level:

Challenge Level:1

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

Powerful Order

KS 3 & 4 Short Challenge Level:

Challenge Level:1

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

Pythagorean Quadruple

KS 3 & 4 Short Challenge Level:

Challenge Level:1

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

Powers of Four

KS 3 & 4 Short Challenge Level:

Challenge Level:1

Weekly Problem 52 - 2007
Can you work out the value of x in this 'power-full' equation?

Rooted Via 10

KS 4 Short Challenge Level:

Challenge Level:2 Challenge Level:2

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

Self-power Squares

KS 4 Short Challenge Level:

Challenge Level:2 Challenge Level:2

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

Largest Expression

KS 4 Short Challenge Level:

Challenge Level:2 Challenge Level:2

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

Doubly Powerful

KS 4 Short Challenge Level:

Challenge Level:2 Challenge Level:2

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

Not a Zero

KS 4 Short Challenge Level:

Challenge Level:2 Challenge Level:2

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

Power of 3

KS 4 Short Challenge Level:

Challenge Level:2 Challenge Level:2

What power of 27 is needed to get the correct power of 3?

Powered Up

KS 4 Short Challenge Level:

Challenge Level:3 Challenge Level:3 Challenge Level:3

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