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Which expression has the same value as [tex]-y^{-4}[/tex]?
A. [tex]-y^4[/tex] B. [tex]-\frac{1}{y^4}[/tex] C. [tex]\frac{1}{y^4}[/tex] D. 4
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]
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