Stacking Bigger and Bigger Powers

Algebra Level 1

$\begin{aligned} \large A &= \frac{9^9}{10^9} \hspace{0.3cm} \\ \\ \hspace{0.3cm} B &= \frac{9^{10}}{10^{10}} \end{aligned}$

Which of these quantities is larger?

A B A and B are equal

1 solution

Eli Ross Staff
Jan 18, 2016

Note that $B = \frac{9}{10} \times A.$

Since $A>0$ but $\frac{9}{10} = 0.9 < 1,$ multiplying $A$ by $0.9$ will give a number less than $A.$

In other words, $B = \frac{9}{10} \times A < A,$

so $A$ is larger than $B.$