To solve the expression \(\frac{5^{11}}{5^{-7}}\) and see if it equals \(5^{18}\), we can start by using the properties of exponents.
The rule for dividing exponents with the same base states that you subtract the exponents:
\[ \frac{a^m}{a^n} = a^{m-n} \]
Applying that to your expression:
\[ \frac{5^{11}}{5^{-7}} = 5^{11 - (-7)} = 5^{11 + 7} = 5^{18} \]
Thus, we have:
\[ \frac{5^{11}}{5^{-7}} = 5^{18} \]
Therefore, the equation is true:
\[ \frac{5^{11}}{5^{-7}} = 5^{18} \]
So \(5^{11} / 5^{-7} = 5^{18}\) is indeed valid.