Gof If? What is the value of \( n^{-4} w^{0} \) for \( n=-2 \) and \( w=5 \) ? Complete each method to solve the problem. 20. Method 1 Simplify first. \( n^{-4} w^{0}=\frac{w^{0}}{} \) Use the definition of negative exponent. \[ \begin{array}{l} =\frac{0}{()^{4}} \\ \text { Substitute } \\ =-\quad \text { Simplify } \end{array} \] 21. Method 2 Substitute first. \( n^{-4} w^{0}=(-2)^{-4} \). \( { }^{0} \). Substitute. \[ \begin{array}{l} =\begin{array}{l} \text { Use the definition of } \\ \text { negative exponent. } \\ = \\ \text { Simplify. } \end{array} \text { } \end{array} \]

Here's a delightful dive into exponents! For Method 1, when we simplify \( n^{-4} w^{0} \), we recall that anything raised to the power of zero is 1. So, \( w^{0} = 1 \)! Now we have \( n^{-4} w^{0} = n^{-4} \cdot 1 \). By the definition of a negative exponent, we can write \( n^{-4} = \frac{1}{n^{4}} \). Substituting \( n = -2 \), we get \( n^{-4} = \frac{1}{(-2)^{4}} = \frac{1}{16} \). Now, on to Method 2! Start with \( n^{-4} w^{0} = (-2)^{-4} \cdot 5^{0} \). Knowing again that \( 5^{0} = 1 \), we can drop that and focus on \( (-2)^{-4} \). Applying the negative exponent rule, \( (-2)^{-4} = \frac{1}{(-2)^{4}} \). Since \( (-2)^{4} = 16 \), we find that \( (-2)^{-4} = \frac{1}{16} \). So, both methods lead us to the conclusion that the value of \( n^{-4} w^{0} \) is \( \frac{1}{16} \). Isn’t math a delight in its consistency?