1993 AMC 12 Problem 3

Attempt Problem 3 of the 1993 AMC 12 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1993 AMC 12 solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

\frac{15^{30}}{45^{15}}=

\left(\frac13\right)^{15}

\left(\frac13\right)^2

1

3^{15}

5^{15}

Write

15^{30}

(15^2)^{15}

Combine the numerator and denominator inside one fifteenth power

Using a common exponent,

\frac{15^{30}}{45^{15}} =\left(\frac{15^2}{45}\right)^{15} =5^{15}.

Thus the correct answer is E.

Problem 3 in other years