28) \( 2^{-n}=8 \)

To solve the equation \( 2^{-n} = 8 \), we start by expressing \( 8 \) as a power of \( 2 \). Since \( 8 = 2^3 \), we can rewrite the equation as \( 2^{-n} = 2^3 \). Because the bases are the same, we can set the exponents equal to each other, yielding \( -n = 3 \). Solving for \( n \), we get \( n = -3 \). Now, if you ever find yourself facing similar exponential equations, remember that converting everything to the same base can simplify the work. It’s like translating a foreign language into one you understand — suddenly, things make much more sense! Just watch out for the negatives; flipping the exponent can sometimes trip you up. For further study, consider exploring logarithms, which are the inverse operations of exponentiation. They're particularly handy when working with more complex equations. You can dive into great resources like "The Joy of x" by Steven Strogatz for an engaging look at mathematical concepts, or search online for practical applications of logarithms in fields like finance and computer science. You'll be a math whiz in no time!