13squareroot 3x4 10k13 64k1216 7 squareroot 640m7 n8 5 squre

1/(3squareroot 3x)^4 (10k)^1/3 (64k^12)^1/6 7 squareroot -640m^7 n^8 5 squreroot 160m^8 n^4 p

Solution

Using the exponential properties for the problems below : 1/a^m = a^-m ; (a^m)^n = a^mn

6. 1/ ((3x)^1/3)^4

=1/(3^4/3*x^4/3

=3^(-4/3)x^(-4/3)

8. (10k)^1/3 = 10^1/3k^1/3

It cannot be simplified further

10. solution is correct

( - 640m^7n^8)^1/7

640 = 2^7*5

= ( -2^7*5m^7n^8)^1/7

= -2(5^1/7)(m)(n^8/7)

= -2m(5n^8)^(1/7)

14 ( 160m^8n^4p)^1/5

=(2^5*5m^8n^4p)^1/5

= 2(5)^1/5(m)^8/5)(n)^4/5)(p)^1/5)