Solve Equations with Exponents

4 3 2 1 0

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 successwith level 2 and 3.

Even with help, students have no success with the unit content.

Focus 4 - Learning Goal #2: Students will work with radicals and integer exponents.

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

√𝟏𝟎𝟎

√𝟏𝟗𝟔

5

10

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

√81

√16

How would you solve an equation if there is an x3?

• 4x3 = 32• x3 = 8

• x = 2

• 6x3 – 7 = 1289• + 7 + 7• 6x3 = 1296• x3 = 216

• x = 6