Algebra

Rules of Exponents: Level 2 Challenges

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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