Question

Simplify: (64x^5y^9z^8)^3/7

Answer 1

( 64 x^5 y^9 z^8 )^(3/7) =
= ( 64 )^(3/7) ( x^5)^(3/7) ( y^9 )^(3/7) ( z^8 )^(3/7) =
= ( 2^6 ) ^(3/7) * x^(15/7) * y^(27/7) * z^(24/7) =
= 2^(18/7) * x^(15/7) * y^(27/7) * z^(24/7) =
= 2^2 * 2^(4/7) * x^2 * x^(1/7) * y^3 * y^(6/7) * z^3 * z^(3/7) =
= 4 * x^2 * y^3 * z^3 * ( 16 * x * y^6 * z^3 )^(1/7) =
=
`4 x^(2) y ^(3) z^(3) \sqrt[7]{16 x y^(6) z ^(3) }`