1994 AMC 12 Problem 1

Attempt Problem 1 of the 1994 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 1994 AMC 12 solutions, or check the answer key.

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

4^4\cdot9^4\cdot4^9\cdot9^9=

13^{13}

13^{36}

36^{13}

36^{36}

1296^{26}

Group the powers of

4

and the powers of

9

Both bases have total exponent

4+9

Combining like bases and then pairing them,

\begin{aligned} 4^4\cdot4^9\cdot9^4\cdot9^9 &=4^{13}9^{13}\\ &=(4\cdot9)^{13}\\ &=36^{13}. \end{aligned}

Thus the correct answer is C.

Problem 1 in other years