Sure! Let's simplify both expressions step-by-step.
### Simplifying Expression for [tex]\( x \)[/tex]:
Given:
[tex]\[ x = x^{12} + 3x^{-2} - \pi x^{-10} \][/tex]
1. Identify parts of the expression:
- [tex]\( x^{12} \)[/tex]
- [tex]\( 3x^{-2} \)[/tex]
- [tex]\( -\pi x^{-10} \)[/tex]
2. Combining components:
- There are no common factors or like terms to combine here. Therefore, the expression is already simplified to its simplest form as:
- [tex]\( x = x^{12} + 3x^{-2} - \pi x^{-10} \)[/tex]
Thus, the simplified expression for [tex]\( x \)[/tex] is:
[tex]\[ x = x^{12} + 3x^{-2} - \pi x^{-10} \][/tex]
### Simplifying Expression for [tex]\( y \)[/tex]:
Given:
[tex]\[ y = \frac{3}{x^3} + x^{-4} \][/tex]
1. Rewrite the terms with negative exponents:
- [tex]\( \frac{3}{x^3} = 3x^{-3} \)[/tex]
So the expression becomes:
[tex]\[ y = 3x^{-3} + x^{-4} \][/tex]
2. Combining components:
- As with the first expression, there are no like terms to combine or common factors to factor out.
Thus, the simplified expression for [tex]\( y \)[/tex] is:
[tex]\[ y = 3x^{-3} + x^{-4} \][/tex]
### Final Answer
The simplified expressions are:
- For [tex]\( x \)[/tex]:
[tex]\[ x = x^{12} + 3x^{-2} - \pi x^{-10} \][/tex]
- For [tex]\( y \)[/tex]:
[tex]\[ y = 3x^{-3} + x^{-4} \][/tex]
