Rules of Exponents

Rules of Exponents: Level 2 Challenges


Which is larger

A=432 or B=234? \large A = 4^ { 3 ^ 2 } \quad \text{ or } \quad B = 2^ { 3 ^ 4 } ?

Let NN be the number of 0's needed to write out 1010000010^{100000}.

How many 0's are needed to write out the number NN?

1!9!2!8!3!7!4!6!5!5! \Large \color{#3D99F6}{1!^{9!}} \hspace{7mm} \color{#20A900}{2!^{8!}} \hspace{7mm} \color{#EC7300}{3!^{7!}} \hspace{7mm} \color{#69047E}{4!^{6!}} \hspace{7mm} \color{#D61F06}{5!^{5!}}

Which of the numbers above is the largest?

27x3+811x4 \huge 27^{- \frac {x}{3} } + 81^{ \frac {1-x}{4} }

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

Which is larger?

107or710 \LARGE \color{#D61F06}{10}^{\color{#3D99F6}{7}} \quad \text{or} \quad \color{#3D99F6}{7}^{\color{#D61F06}{10}}


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