To solve the equation \(\frac{7^{8}}{7^{10}}=7^{x}\), we can use the properties of exponents.
According to the property of exponents, when you divide two expressions with the same base, you subtract the exponents:
\[ \frac{a^m}{a^n} = a^{m-n} \]
Applying this to our expression:
\[ \frac{7^{8}}{7^{10}} = 7^{8-10} = 7^{-2} \]
Now we have:
\[ 7^{-2} = 7^{x} \]
Since the bases are the same, we can set the exponents equal to each other:
\[ -2 = x \]
Thus, the missing exponent \(x\) is:
\[ \boxed{-2} \]