Certainly! Let's solve the expression [tex]\( x \cdot y^{-1} \)[/tex] step by step.
1. Understand the notation:
- The notation [tex]\( y^{-1} \)[/tex] represents the multiplicative inverse (reciprocal) of [tex]\( y \)[/tex]. This means [tex]\( y^{-1} = \frac{1}{y} \)[/tex].
2. Rewrite the expression:
- Since [tex]\( y^{-1} = \frac{1}{y} \)[/tex], we can rewrite [tex]\( x \cdot y^{-1} \)[/tex] as [tex]\( x \cdot \frac{1}{y} \)[/tex].
3. Simplify the multiplication:
- When you multiply [tex]\( x \)[/tex] by [tex]\( \frac{1}{y} \)[/tex], it's equivalent to dividing [tex]\( x \)[/tex] by [tex]\( y \)[/tex]. That is, [tex]\( x \cdot \frac{1}{y} = \frac{x}{y} \)[/tex].
4. Assign values and calculate:
- Let's assign the given values [tex]\( x = 10 \)[/tex] and [tex]\( y = 5 \)[/tex] and calculate the result.
- Substituting these values into the simplified expression, we get [tex]\( \frac{10}{5} \)[/tex].
5. Perform the division:
- [tex]\( \frac{10}{5} \)[/tex] equals [tex]\( 2 \)[/tex].
Hence, the result of the expression [tex]\( x \cdot y^{-1} \)[/tex] is [tex]\( 2 \)[/tex].
