Consider the following function.
\[
F(t)=\left(\frac{1}{5 t+1}\right)^{3}
\]
Simplify by rewriting $F(t)$ using a negative exponent and no fractions.
\[
F(t)=
\]
Find the derivative of the sirnplified function.
\[
F^{\prime}(t)=
\]
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Step 1 ：Simplify the function $F(t)$ by rewriting it using a negative exponent and no fractions. This can be done by applying the rule $a^{-n} = \frac{1}{a^n}$, which allows us to rewrite the function as $F(t) = (5t + 1)^{-3}$.

Step 2 ：Find the derivative of the simplified function. This can be done by applying the chain rule, which states that the derivative of a composite function is the derivative of the outer function times the derivative of the inner function. In this case, the outer function is $x^{-3}$ and the inner function is $5t + 1$.

Step 3 ：The simplified function is $F(t) = \boxed{(5t + 1)^{-3}}$ and its derivative is $F^{\prime}(t) = \boxed{-\frac{15}{(5t + 1)^4}}$