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# Rules of Exponents

Adding 10 to itself 10 times gives 100, but how can we represent 10 multiplied to itself 10 times?

Which is larger

\[ \large A = 4^ { 3 ^ 2 } \quad \text{ or } \quad B = 2^ { 3 ^ 4 } ? \]

Let \(N\) be the number of 0's needed to write out \(10^{100000}\).

How many 0's are needed to write out the number \(N\)?

\[ \Large \color{blue}{1!^{9!}} \hspace{7mm} \color{green}{2!^{8!}} \hspace{7mm} \color{orange}{3!^{7!}} \hspace{7mm} \color{purple}{4!^{6!}} \hspace{7mm} \color{red}{5!^{5!}}\]

Which of the numbers above is the largest?

\[ \huge 27^{- \frac {x}{3} } + 81^{ \frac {1-x}{4} } \]

If the expression above can be stated in the form of \( \dfrac {a}{b^x} \) for positive integers \(a\) and \(b\), what is the value of \(a+b\)?

Which is larger?

\[ \LARGE \color{red}{10}^{\color{blue}{7}} \quad \text{or} \quad \color{blue}{7}^{\color{red}{10}} \]

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