Help. ​

3.

³√ [ 4x^2  *  ³ √ [ 8x^7 ]    =

³√ [  4* 8  x^2  x^7 ]  =

³√ [ 32  x^9 ]  =                            {note that 32  = 2^5 ]

³√  [ 2^5 x^9 ]

To determine how many powers of 2 to take out and how many to leave in, we have

5/3   =  1  + 2/3          1 power of 2 comes out and 2 stay in

To determine how many powers of x come out and how many stay in, we have

9 / 3   =  3  powers come out      .....    so we end up with

 2 x^3 ³√ [2^2]     =    2x^3 *  ³√ 4  

4.

⁴√ 810

______    =      ⁴ √ [ 810 / 2]    =  ⁴√405   = ⁴ √ [ 81 * 5 ]  = ⁴√81   * ⁴√5

⁴√2

Note that 81  =  3^4   ....so we have...

⁴√81  * ⁴√ 5      =

⁴√ [ 3^4] *  ⁴√5    =

To determine how many powers of 3 to take out    4/4  =  1 power of 3

3 ⁴√5