Indices

There are 41 NRICH Mathematical resources connected to Indices
Tens
problem
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Tens

Age
16 to 18
Challenge level
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When is $7^n + 3^n$ a multiple of 10? Can you prove the result by two different methods?
Negative Power
problem
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Negative power

Age
14 to 16
Challenge level
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What does this number mean ? Which order of 1, 2, 3 and 4 makes the highest value ? Which makes the lowest ?
Telescoping series
problem
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Telescoping series

Age
16 to 18
Challenge level
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Find $S_r = 1^r + 2^r + 3^r + ... + n^r$ where r is any fixed positive integer in terms of $S_1, S_2, ... S_{r-1}$.
Power Quady
problem
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Power quady

Age
16 to 18
Challenge level
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Find all real solutions of the equation (x^2-7x+11)^(x^2-11x+30) = 1.
Climbing Powers
problem
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Climbing powers

Age
16 to 18
Challenge level
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$2\wedge 3\wedge 4$ could be $(2^3)^4$ or $2^{(3^4)}$. Does it make any difference? For both definitions, which is bigger: $r\wedge r\wedge r\wedge r\dots$ where the powers of $r$ go on for ever, or $(r^r)^r$, where $r$ is $\sqrt{2}$?
Sums of Squares
problem
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Sums of squares

Age
16 to 18
Challenge level
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Can you prove that twice the sum of two squares always gives the sum of two squares?
How Many Solutions?
problem
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How many solutions?

Age
16 to 18
Challenge level
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Find all the solutions to the this equation.
Perfectly Square
problem
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Perfectly square

Age
14 to 16
Challenge level
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The sums of the squares of three related numbers is also a perfect square - can you explain why?
Giants
problem
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Giants

Age
16 to 18
Challenge level
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Which is the bigger, 9^10 or 10^9 ? Which is the bigger, 99^100 or 100^99 ?
Rachel's Problem
problem

Rachel's problem

Age
14 to 16
Challenge level
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Is it true that $99^n$ has 2n digits and $999^n$ has 3n digits? Investigate!