Solving Equations with Fractional Powers Reminder about powers: Means = 5 Means = 3 Means = 3 2 = 9

= 7 = 2 = 2 2 = 4 = 2 3 = 8 Reminder about powers:

this means the cube root of x equals 3 To solve this equation do the opposite of cube root i.e cube so that Solving Equations with Fractional Powers x = 3 3 = 27

this means the fourth root of x equals 5 To solve this equation do the opposite of 4 th root so that x = 5 4 i.e raise it to the power of 4 = 625

this means find the square root of x and then cube it To solve this equation do the opposite so that x = So the rule is flip the power and apply it to the other side. i.e. cube root it and square

flip power x = 16 Find 5 th root and then raise it to power 4 As 2x2x2x2x2 = 32 As 2x2x2x2 = 16 x = 2 4

Go forwards flip power x = 2 4 = 16 i.e cube root of 8 raised to power 4 Go backwards

Flip power change the line, change the sign Go forwards Go backwards

General Method Flip power Go forwards Go backwards

Using a calculator Use the power and then fraction button on calculator x = to 2d.p flip power Go forwards Go backwards

Converting to a power question x  cube root  square  ×3 =  ÷3  square root  cube = x