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?