Question

Rewrite the following expression with rational exponents. 3 sq root -27x^2 y^7
Show your work

Answer 1

Explanation:

The square root is possible only if y≤0

if y>0 the expression lose meaning, in fact (-)(+)(+) = (-) and a square root of a negative number doesn’t exist. x^2 is a square so it is ever positive if x is not 0

if y≤0 can be rewritten as:

3(-27x^2y^7)^1/2

or if we want simplify the expression:

`3 √(3^2 * (-3) * x^2 * y^6 * y) = 3^2|x||y|^3 (-3y)` ^1/2

we have to put the symbol of absolute value between x and y because a x^2 and y^6 are numbers that are ever positive, while x and y^3 can be also negative. Thanks to the simbol of absolute value we can “force” them to be positive