To find by what number [tex]\((-3 / 2)^{-3}\)[/tex] should be multiplied so that the product is [tex]\((98)^{-2}\)[/tex], we need to follow these steps:
1. Calculate [tex]\((-3 / 2)^{-3}\)[/tex]:
[tex]\[
(-3 / 2)^{-3} \approx -0.2962962962962963
\][/tex]
2. Calculate [tex]\((98)^{-2}\)[/tex]:
[tex]\[
(98)^{-2} \approx 0.00010412328196584757
\][/tex]
3. Determine the multiplication factor that transforms [tex]\((-3 / 2)^{-3}\)[/tex] into [tex]\((98)^{-2}\)[/tex].
This factor can be found by dividing [tex]\((98)^{-2}\)[/tex] by [tex]\((-3 / 2)^{-3}\)[/tex]:
[tex]\[
\text{Multiplication factor} = \frac{(98)^{-2}}{(-3 / 2)^{-3}}
\][/tex]
4. Using the previously calculated values:
[tex]\[
\text{Multiplication factor} = \frac{0.00010412328196584757}{-0.2962962962962963} \approx -0.00035141607663473557
\][/tex]
Therefore, [tex]\((-3 / 2)^{-3}\)[/tex] should be multiplied by approximately [tex]\(-0.00035141607663473557\)[/tex] so that the product is [tex]\((98)^{-2}\)[/tex].
