Which expression has the same value as \( -y^{-4} \) ? \( -\frac{y^{4}}{-\frac{1}{y^{4}}} \) \( \frac{1}{y^{4}} \) \( y^{4} \)

We begin with the given expression: \[ -y^{-4} \] Recall that a negative exponent means: \[ y^{-4} = \frac{1}{y^4} \] Thus, we can rewrite the expression as: \[ -y^{-4} = -\frac{1}{y^4} \] Now, we will compare this with each of the provided options. **Option 1:** \[ -\frac{y^4}{-\frac{1}{y^4}} \] First, note that the two negative signs in the numerator and denominator cancel: \[ -\frac{y^4}{-\frac{1}{y^4}} = \frac{y^4}{\frac{1}{y^4}} \] Dividing by a fraction is equivalent to multiplying by its reciprocal: \[ \frac{y^4}{\frac{1}{y^4}} = y^4 \cdot y^4 = y^8 \] This is not equivalent to \(-\frac{1}{y^4}\). **Option 2:** \[ \frac{1}{y^4} \] This expression is positive, whereas our simplified expression is negative. Therefore, \[ \frac{1}{y^4} \neq -\frac{1}{y^4} \] **Option 3:** \[ y^4 \] This expression does not match the form \(-\frac{1}{y^4}\), as it is completely different. Since none of the given options simplifies to \(-\frac{1}{y^4}\), we conclude that none of the provided expressions is equivalent to \( -y^{-4} \).