#### Understanding

This lesson allows students to investigate how patterns they developed for postive exponents extend to integer exponents.

### What to look for

Common misconceptions include not understanding which element in the expression is the base of the exponent, multiplying the exponent and the base, reversing the role of the base and the exponent, and assuming a negative exponent changes the sign of the base.

### Sample Assessment

Which of the following expressions are equivalent to \(\frac{3^{-8}}{3^{-4}}\)?a. \(3^{-12}\) b. \(3^4\) c. \(3^2\)

d. \(\frac{1}{3^2}\) e. \(\frac{1}{3^4}\) f. \(\frac{1}{3^{12}}\)

Answer: b and e