Solve Equations with Exponents

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Presentation transcript:

Solve Equations with Exponents

Focus 4 - Learning Goal #2: Students will work with radicals and integer exponents. 3 2 1 In addition to level 3.0 and above and beyond what was taught in class, students may: - Make connection with other concepts in math - Make connection with other content areas. Students will work with radicals and integer exponents. - Use square root & cube root symbols to solve equations in the form x2 = p and x3 = p. - Evaluate roots of small perfect square. - Evaluate roots of small cubes. - Apply square roots & cube roots as it relates to volume and area of cubes and squares. Students will be able to: - Understand that taking the square root & squaring are inverse operations. - Understand that taking the cube root & cubing are inverse operations. With help from the teacher, I have partial success with level 2 and 3. Even with help, students have no success with the unit content.

How do you solve an equation? 5x – 9 = 21 +9 +9 5x = 30 5 5 x = 6 We will use order of operations backwards: Add or Subtract Multiply or Divide Exponents Parenthesis To get rid of subtracting we use the inverse operation which is adding. Inverse operation means to do the opposite operation.

What about exponents? What is the inverse operation of squaring a number? The inverse operation is to square root the number. Try solving the following equations: x2 = 25 x = y2 = 100 y = z2 = 196 z = 𝟐𝟓 5 𝟏𝟎𝟎 10 𝟏𝟗𝟔 14

Try a few more equations: x2 – 9 = 27 + 9 +9 x2 = 36 x = 6 2y2 + 11 = 173 - 11 -11 2y2 = 162 y2 = 81 y = 9 3m2 – 4 = 22 2 3m2 – 4 = 44 + 4 + 4 3m2 = 48 m2 = 16 m = 4 36 16 81

How would you solve an equation if there is an x3? 3 8 x = 2 6x3 – 7 = 1289 + 7 + 7 6x3 = 1296 x3 = 216 3 216 x = 6