An engineering technician is simplifying a complex ratio used in load-bearing calculations: $\frac{3a^2-8a-3}{a^2-25} \cdot \frac{a^2+10a+25}{3a^2-14a-5}$. Arrange the following steps in the correct order to multiply these rational expressions according to the standard mathematical procedure.

An inventory specialist at a logistics company is simplifying a ratio representing shipping efficiency: $\frac{3a^2-8a-3}{a^2-25} \cdot \frac{a^2+10a+25}{3a^2-14a-5}$. According to the standard mathematical procedure for multiplying rational expressions involving trinomials, what is the first required step?

A technical analyst at a manufacturing firm is verifying a safety-ratio calculation used for stress-testing equipment: $\frac{3a^2-8a-3}{a^2-25} \cdot \frac{a^2+10a+25}{3a^2-14a-5}$. To confirm the accuracy of the simplification process, match each algebraic expression from this calculation with its correct completely factored form as shown in the standard procedure.

A quality control specialist is auditing a series of algebraic formulas used in manufacturing, including the product: $\frac{3a^2-8a-3}{a^2-25} \cdot \frac{a^2+10a+25}{3a^2-14a-5}$. True or False: In the final stage of simplifying this expression, if the result contains repeated factors like $(a-5)(a-5)$, the standard procedure is to rewrite them using an exponent, such as $(a-5)^2$.

A logistics coordinator is following a standardized procedure to simplify efficiency ratios, which involves multiplying rational expressions like $\frac{3a^2-8a-3}{a^2-25} \cdot \frac{a^2+10a+25}{3a^2-14a-5}$. In the final step of this procedure, after factoring and dividing out common factors to reach $\frac{(a-3)(a+5)}{(a-5)(a-5)}$, the coordinator must rewrite any repeated factors using an ________, producing the final simplified form $\frac{(a-3)(a+5)}{(a-5)^2}$.