Sure! Let's work through the evaluation of the expression [tex]\(3 x^{-2} y\)[/tex] step by step, assuming we are given specific values for [tex]\(x\)[/tex] and [tex]\(y\)[/tex].
Let's say [tex]\(x = 2\)[/tex] and [tex]\(y = 5\)[/tex].
Now, follow these steps:
1. Calculate [tex]\(x^{-2}\)[/tex]:
- Since [tex]\(x = 2\)[/tex], we have [tex]\(x^{-2} = (2)^{-2}\)[/tex].
- [tex]\( (2)^{-2} \)[/tex] means we need to take the reciprocal of [tex]\(2\)[/tex] and then square it.
- Reciprocally, [tex]\(2\)[/tex] becomes [tex]\( \frac{1}{2} \)[/tex].
- Squaring [tex]\( \frac{1}{2} \)[/tex] gives us [tex]\( \left(\frac{1}{2}\right)^2 = \frac{1}{4} \)[/tex].
- So, [tex]\(2^{-2} = \frac{1}{4}\)[/tex].
2. Multiply this result by the coefficient [tex]\(3\)[/tex]:
- We have [tex]\(3 \cdot \frac{1}{4}\)[/tex].
- Multiplying [tex]\(3\)[/tex] by [tex]\( \frac{1}{4} \)[/tex] gives us [tex]\( \frac{3}{4} \)[/tex] or [tex]\(0.75\)[/tex].
3. Multiply the above result by [tex]\(y\)[/tex]:
- Given [tex]\(y = 5\)[/tex], we multiply [tex]\(0.75\)[/tex] by [tex]\(5\)[/tex].
- So, [tex]\(0.75 \times 5 = 3.75\)[/tex].
Therefore, after following these steps and substituting the given values, we find that the value of the expression [tex]\(3 x^{-2} y\)[/tex] when [tex]\(x = 2\)[/tex] and [tex]\(y = 5\)[/tex] is indeed [tex]\(3.75\)[/tex].
