Art of Problem Solving
AoPS Online
Math texts, online classes, and more
for students in grades 5-12.
Visit AoPS Online ‚
Books for Grades 5-12 Online Courses
Beast Academy
Engaging math books and online learning
for students ages 6-13.
Visit Beast Academy ‚
Books for Ages 6-13 Beast Academy Online
AoPS Academy
Small live classes for advanced math
and language arts learners in grades 2-12.
Visit AoPS Academy ‚
Find a Physical Campus Visit the Virtual Campus
During AMC testing, the AoPS Wiki is in read-only mode and no edits can be made.

1998 CEMC Pascal Problems/Problem 5

Problem

The value of $\frac{5^6 \times 5^9 \times 5}{5^3}$ is

$\text{ (A) }\ 5^{18} \qquad\text{ (B) }\ 25^{18} \qquad\text{ (C) }\ 5^{13} \qquad\text{ (D) }\ 25^{13} \qquad\text{ (E) }\ 5^{51}$

Solution

We can use the fact that $a^{b + c} = a^{b} \times a^{c}$, and $a^{b - c} = \frac{a^{b}}{a^{c}}$:

$\frac{5^6 \times 5^9 \times 5}{5^3} = \frac{5^{6 + 9} \times 5^{1}}{5^3} = \frac{5^{6 + 9 + 1}}{5^3}$

$=\frac{5^{16}}{5^3} = 5^{16 - 3} = \boxed {\textbf {(C) } 5^{13}}$

~anabel.disher

Retrieved from "https://artofproblemsolving.com/wiki/index.php?title=1998_CEMC_Pascal_Problems/Problem_5&oldid=251864"