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To simplify the expression \( \frac{7^{21}}{7^{18}} \), you can use the properties of exponents. When you divide two exponents with the same base, you subtract the exponents:

\[ \frac{a^m}{a^n} = a^{m-n} \]

Applying this to your expression:

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

Now, \( 7^3 \) can be calculated as:

\[ 7^3 = 7 \times 7 \times 7 = 343 \]

Thus, the simplified expression equates to:

\[ \frac{7^{21}}{7^{18}} = 7^3 = 343 \]