What Do You Notice?
Complete the table below paying attention to the patterns you discover (complete Lesson 1 for information on expressions with integer exponents).
| Exponential Form | Expanded Form | Simplified Form |
| \(5^2\cdot5^3\) | ||
| \(x^3\cdot x^4\) | ||
| \(3x^2\cdot2x^4\) | ||
| \(5x^3\cdot 3x^{-2}\) | ||
| \((3^2)^4\) | ||
| \((x^3)^2\) | ||
| \((2x^3)^2\) | ||
| \((2x^2y^3)^3\) | ||
| \(\bigg(\dfrac{3x}{y^2}\bigg)^3\) |
What patterns do you notice?
How could you generalize these patterns?
