Lesson Plan

Rewrite expressions containing exponents or radicals in equivalent forms, using the exponent rules with integer, zero, negative, rational and variable exponents

Derive the product, quotient, power-of-a-power and power-of-a-product rules from repeated multiplication, and identify expressions they do not combine ($x^3 + x^3$, $2^3 \cdot 3^2$)

Explain $b^0 = 1$ and $b^{-n} = \frac{1}{b^n}$ ($b \ne 0$) as the values that keep the quotient rule true

Convert between rational-exponent and radical form in both directions using $a^{m/n} = (\sqrt[n]{a})^m = \sqrt[n]{a^m}$, and evaluate rational powers of numbers

Simplify square and cube roots by extracting the largest perfect-power factor

"Make strategic use of algebraic structure and the properties of operations to identify and create equivalent expressions" "• including rewriting simple rational expressions, rewriting expressions with rational exponents in radical form, and factoring polynomials not included in the preceding bullet."