Worksheet Worksheet 2
1.
Calculate \(x^{-2} \cdot x^{-3}\) using a presentation that shows all of the individual steps. Then verify that the product rule gives the same result.
2.
Calculate \(\left( x^{-1} \right)^{-n}\) using the power rule. Then rewrite the part of the expression inside the parentheses using the definition of negative exponents. In order for the math to be consistent, the two results should be equal. Explain how this verifies the first formula in Theorem 6.1.4.
3.
Start from the equation \(x^{-n} = \frac{1}{x^n}\) and take the reciprocal of both sides of the equation. Explain how this verifies the second formula in Theorem 6.1.4.