Question

Simplify. −64x6y9−−−−−−−√3 assume all variables are nonnegative.

Answer 1

In this item, I take it that we are to get  the cube root of the given expression, -64x6y9. First, we look into the numerical coefficient, this is the product when -4 is multiplied to itself three times as shown below.

    -64 = (-4)(-4)(-4)

Then, 
   x6 = x2 (x2) (x2)

and,
    y9 = (y3)(y3)(y3)

If we take the cube root, we consider only one item per product. Thus, the answer is,
    
    -4x²y³

Answer 2

Answer:

$-4x^2y^3$

Step-by-step explanation:

We have been given an expression $\sqrt[3]{-64x^6y^9}$. We are asked to simplify our given expression.

Applying radical rule $\sqrt[n]{-a}=-\sqrt[n]{a}$, when n is odd, we will get:

$-\sqrt[3]{64x^6y^9}$

We can rewrite terms of our given expression as:

$-\sqrt[3]{(4)^3(x^2)^3(y^3)^3}$

Using radical rule $\sqrt[n]{a^n}=a$, we will get:

$-4x^2y^3$

Therefore, simplified form of our given expression is $-4x^2y^3$.