Submitted by Speedscarlet on Wed, 11/30/2016 - 23:27
Forums:
2000(2000^2000) without calculator
Help please
Submitted by Speedscarlet on Wed, 11/30/2016 - 23:27
2000(2000^2000) without calculator
Help please
Underground Mathematics: Selected worked STEP questions
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University of Cambridge Mathematics Faculty: Information about STEP
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MEI: Worked solutions to STEP questions (external link)
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AMSP (Advanced Maths Support programme): Support for University Admission Tests (external link)
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What sort of form do you want
What sort of form do you want to get this into? Presumably you want to simplify it rather than write out all it's decimal digits? If so, remember the fact that $a^m \cdot a^k = a^{m+k}$ for all $m,k$ and a given $a$. This can be "shown" (note it's not an actual proof, it only holds for integer $m$ and $k$) by writing out the terms like so:
$$a^m \cdot a^k = \underbrace{a\cdot a\cdots a}_{m \, \text{times}} \cdot \underbrace{a \cdot a \cdots a}_{k \, \text{times}} = \underbrace{a \cdot a \cdot a \cdots a}_{(m+k) \, \text{times}} = a^{m+k}$$
Can you spot what $(a,m,k) = (?,?,?)$ you have in your problem?