Challenge Level

$4^x=9$ can be substituted into $9^y=64$, giving $\left(4^x\right)^y=64$.

Finding a power of a power of a number is the same as multiplying the powers, so $\left(4^x\right)^y=4^{xy}$. So $4^{xy}=64$.

$4^1=4$

$4^2=16$

$4^3=16\times4=64$

So $xy=3$.

You can find more short problems, arranged by curriculum topic, in our short problems collection.