Answer :
To determine which expression has the same value as \(-y^{-4}\), let's break down the given options step-by-step.
First, let's understand what \(-y^{-4}\) represents.
1. Exponent Negative Power Rule: \( y^{-n} = \frac{1}{y^n} \). So, \(-y^{-4} = - \frac{1}{y^4} \).
We need to compare this with the given options:
1. Option 1: \(-y^4\)
- This expression means the negative of \(y\) raised to the power of 4, which is \(-y^4\).
- Example Calculation (if \(y = 2\)): \(-2^4 = -16\).
2. Option 2: \(-\frac{1}{y^4}\)
- This expression represents the negative reciprocal of \(y\) raised to the power of 4, which is \(-\frac{1}{y^4} \).
- Example Calculation (if \(y = 2\)): \(-\frac{1}{2^4} = -\frac{1}{16} = -0.0625\).
3. Option 3: \(\frac{1}{y^4}\)
- This expression means the reciprocal of \(y\) raised to the power of 4, which is \(\frac{1}{y^4} \).
- Example Calculation (if \(y = 2\)): \(\frac{1}{2^4} = \frac{1}{16} = 0.0625\).
4. Option 4: \(4\)
- This expression is simply the number 4.
- Example Calculation: It remains \(4\), independent of \(y\).
Now, we compare these outcomes with the value of \(-y^{-4}\):
- We calculated \(-y^{-4}\) to be \(-\frac{1}{y^4}\), which matches Option 2.
Hence, the expression that has the same value as \(-y^{-4}\) is:
[tex]\[ \boxed{-\frac{1}{y^4}} \][/tex]
First, let's understand what \(-y^{-4}\) represents.
1. Exponent Negative Power Rule: \( y^{-n} = \frac{1}{y^n} \). So, \(-y^{-4} = - \frac{1}{y^4} \).
We need to compare this with the given options:
1. Option 1: \(-y^4\)
- This expression means the negative of \(y\) raised to the power of 4, which is \(-y^4\).
- Example Calculation (if \(y = 2\)): \(-2^4 = -16\).
2. Option 2: \(-\frac{1}{y^4}\)
- This expression represents the negative reciprocal of \(y\) raised to the power of 4, which is \(-\frac{1}{y^4} \).
- Example Calculation (if \(y = 2\)): \(-\frac{1}{2^4} = -\frac{1}{16} = -0.0625\).
3. Option 3: \(\frac{1}{y^4}\)
- This expression means the reciprocal of \(y\) raised to the power of 4, which is \(\frac{1}{y^4} \).
- Example Calculation (if \(y = 2\)): \(\frac{1}{2^4} = \frac{1}{16} = 0.0625\).
4. Option 4: \(4\)
- This expression is simply the number 4.
- Example Calculation: It remains \(4\), independent of \(y\).
Now, we compare these outcomes with the value of \(-y^{-4}\):
- We calculated \(-y^{-4}\) to be \(-\frac{1}{y^4}\), which matches Option 2.
Hence, the expression that has the same value as \(-y^{-4}\) is:
[tex]\[ \boxed{-\frac{1}{y^4}} \][/tex]
