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Resources tagged with Powers & roots similar to Rolling Along the Trail:

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Broad Topics > Numbers and the Number System > Powers & roots

Diggits

Stage: 3 Challenge Level:

Can you find what the last two digits of the number $4^{1999}$ are?

Largest Number

Stage: 3 Challenge Level:

What is the largest number you can make using the three digits 2, 3 and 4 in any way you like, using any operations you like? You can only use each digit once.

Like Powers

Stage: 3 Challenge Level:

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.

Two Many

Stage: 3 Challenge Level:

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

Lastly - Well

Stage: 3 Challenge Level:

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

Stage: 3 Challenge Level:

Powers of numbers behave in surprising ways. Take a look at some of these and try to explain why they are true.

Sept 03

Stage: 3 Challenge Level:

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

Magic Potting Sheds

Stage: 3 Challenge Level:

Mr McGregor has a magic potting shed. Overnight, the number of plants in it doubles. He'd like to put the same number of plants in each of three gardens, planting one garden each day. Can he do it?

More Magic Potting Sheds

Stage: 3 Challenge Level:

The number of plants in Mr McGregor's magic potting shed increases overnight. He'd like to put the same number of plants in each of his gardens, planting one garden each day. How can he do it?

Power Crazy

Stage: 3 Challenge Level:

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?

St Ives

Stage: 2

As I was going to St Ives, I met a man with seven wives. Every wife had seven sacks, every sack had seven cats, every cat had seven kittens. Kittens, cats, sacks and wives, how many were going to St. . . .

Sissa's Reward

Stage: 3 Challenge Level:

Sissa cleverly asked the King for a reward that sounded quite modest but turned out to be rather large...