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1998 CEMC Pascal Problems/Problem 5

Revision as of 17:05, 22 June 2025 by Anabel.disher (talk | contribs) (1)
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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

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