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Learning Goal

‹4 of 6 in this skill_area›

Exponent rules and radical-exponent conversion

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Lesson Plan · Guided Notes · Exit Ticket · Re-teach · Homework

"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."

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"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."

What you'll learn

  1. Rewrite expressions containing exponents or radicals in equivalent forms, using the exponent rules with integer, zero, negative, rational and variable exponents
  2. Derive the product, quotient, power-of-a-power and power-of-a-product rules from repeated multiplication, and identify expressions they do not combine ($x^3 + x^3$, $2^3 \cdot 3^2$)
  3. Explain $b^0 = 1$ and $b^{-n} = \frac{1}{b^n}$ ($b \ne 0$) as the values that keep the quotient rule true
  4. 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
  5. Simplify square and cube roots by extracting the largest perfect-power factor

Slides

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