Question

What is 125^2/3 in simplest form? and What is \sqrt[5]({-245} ) ^{5} in simplest form?

Answer 1

${ 125 }^{ \frac { 2 }{ 3 } }\\ \\ ={ \left( { 125 }^{ \frac { 1 }{ 3 } } \right) }^{ 2 }\\ \\ ={ \left( \sqrt [ 3 ]{ 125 } \right) }^{ 2 }\\ \\ ={ 5 }^{ 2 }\\ \\ =25$

This is because:

${ a }^{ \frac { m }{ n } }\\ \\ =\sqrt [ n ]{ { a }^{ m } }$

Remember that:

5 x 5 x 5 = 125