To determine which of the given expressions are equivalent to the original expression [tex]\( y^3 y^3 x^0 x^{-2} \)[/tex], let's go through each step carefully and analyze the expression.
### Step-by-Step Solution:
1. Start with the original expression:
[tex]\[ y^3 y^3 x^0 x^{-2} \][/tex]
2. Simplify the expression:
- Combine the [tex]\( y \)[/tex] terms:
[tex]\[ y^3 \cdot y^3 = y^{3+3} = y^6 \][/tex]
- Combine the [tex]\( x \)[/tex] terms:
[tex]\[ x^0 \cdot x^{-2} = x^{0+(-2)} = x^{-2} \][/tex]
- Therefore, the simplified form of the expression is:
[tex]\[ y^6 x^{-2} \][/tex]
3. Compare the simplified expression with the list of given expressions:
- [tex]\( x^2 y^{-11} \)[/tex]:
- The simplified expression is [tex]\( y^6 x^{-2} \)[/tex].
- [tex]\( x^2 y^{-11} \)[/tex] does not match [tex]\( y^6 x^{-2} \)[/tex].
- [tex]\( \frac{1}{z^2 y^5} \)[/tex]:
- The simplified expression is [tex]\( y^6 x^{-2} \)[/tex].
- [tex]\( \frac{1}{z^2 y^5} \)[/tex] does not match [tex]\( y^6 x^{-2} \)[/tex].
- [tex]\( \frac{1}{y^{2 x}} \)[/tex]:
- The simplified expression is [tex]\( y^6 x^{-2} \)[/tex].
- [tex]\( \frac{1}{y^{2 x}} \)[/tex] does not match [tex]\( y^6 x^{-2} \)[/tex].
- [tex]\( \frac{x^2}{y^{12}} \)[/tex]:
- The simplified expression is [tex]\( y^6 x^{-2} \)[/tex].
- [tex]\( \frac{x^2}{y^{12}} \)[/tex] does not match [tex]\( y^6 x^{-2} \)[/tex].
- [tex]\( y^{-24} \)[/tex]:
- The simplified expression is [tex]\( y^6 x^{-2} \)[/tex].
- [tex]\( y^{-24} \)[/tex] does not match [tex]\( y^6 x^{-2} \)[/tex].
- [tex]\( z^{-2} y^{-5} \)[/tex]:
- The simplified expression is [tex]\( y^6 x^{-2} \)[/tex].
- [tex]\( z^{-2} y^{-5} \)[/tex] does not match [tex]\( y^6 x^{-2} \)[/tex].
### Conclusion:
Upon reviewing and simplifying the given expression, none of the provided expressions match the simplified form [tex]\( y^6 x^{-2} \)[/tex]. Therefore, the expressions equivalent to the given expression [tex]\( y^3 y^3 x^0 x^{-2} \)[/tex] are:
[tex]\[ [\text{None of these}] \][/tex]
So, the result is:
[tex]\[ [False, None, False, False, None, None] \][/tex]
None of the provided expressions are equivalent to [tex]\( y^6 x^{-2} \)[/tex].
