3^18•7^18/21^19=?

To simplify the expression \( \frac{3^{18} \cdot 7^{18}}{21^{19}} \), we first rewrite \( 21 \) in terms of its prime factors:

\[ 21 = 3 \cdot 7 \]

Now, we can express \( 21^{19} \) as:

\[ 21^{19} = (3 \cdot 7)^{19} = 3^{19} \cdot 7^{19} \]

Next, we can substitute this back into the original expression:

\[ \frac{3^{18} \cdot 7^{18}}{21^{19}} = \frac{3^{18} \cdot 7^{18}}{3^{19} \cdot 7^{19}} \]

Now, we can simplify the fraction by applying the rules of exponents. For \( 3^{18} \) over \( 3^{19} \), we have:

\[ \frac{3^{18}}{3^{19}} = 3^{18 - 19} = 3^{-1} \]

For \( 7^{18} \) over \( 7^{19} \), we have:

\[ \frac{7^{18}}{7^{19}} = 7^{18 - 19} = 7^{-1} \]

Combining these results together, we get:

\[ \frac{3^{18} \cdot 7^{18}}{3^{19} \cdot 7^{19}} = 3^{-1} \cdot 7^{-1} = \frac{1}{3} \cdot \frac{1}{7} = \frac{1}{21} \]

Thus, the final answer is:

\[ \frac{3^{18} \cdot 7^{18}}{21^{19}} = \frac{1}{21} \]