Let's simplify the given expression step-by-step:
### Expression
The given expression is:
[tex]\[ x^{-4} y^2 \][/tex]
### Step-by-Step Solution
1. Understand the Exponents:
- [tex]\( x^{-4} \)[/tex] indicates that [tex]\( x \)[/tex] is raised to the power of [tex]\(-4\)[/tex].
- [tex]\( y^2 \)[/tex] indicates that [tex]\( y \)[/tex] is raised to the power of [tex]\( 2 \)[/tex].
2. Simplify Each Component Separately:
- [tex]\[ x^{-4} \][/tex]
- A negative exponent means we take the reciprocal of the base and change the exponent to positive. Therefore:
[tex]\[ x^{-4} = \frac{1}{x^4} \][/tex]
- [tex]\[ y^2 \][/tex]
- This term means [tex]\( y \)[/tex] raised to the power of [tex]\( 2 \)[/tex], which remains as it is:
[tex]\[ y^2 \][/tex]
3. Combine the Simplified Components:
- Now, we combine both simplified terms:
[tex]\[ \frac{1}{x^4} \cdot y^2 \][/tex]
4. Final Expression:
- Write the combined expressions together:
[tex]\[ \frac{y^2}{x^4} \][/tex]
### Summary
The expression [tex]\( x^{-4} y^2 \)[/tex] simplifies to:
[tex]\[ \frac{y^2}{x^4} \][/tex]
This is the simplified form of the given expression.
