simplify:(3x0 ynegative 4)(2x2 y)3 this is hard to break down but i got 6x6/y but my sister said it could either be 24x6/y or 216x6/y6 if not any break it down and tell me which one is right thank u please keep it clear and simple so i can understand

Responses

algebra - bobpursley, Monday, August 18, 2008 at 9:05am
I get a coefficent of 24, with the x,y as you did. I think you forgot to cube the 2 in the second parenthesis.

so the answer is 6x6/y or 24x6/y

To simplify the expression (3x^0y^-4)(2x^2y)^3, we need to follow a few steps.

Step 1: Simplify inside the parentheses first. In the second set of parentheses, we have (2x^2y)^3. To simplify this, we need to raise each term inside the parentheses to the power of 3. So we have:
(2x^2y)^3 = 2^3 * (x^2)^3 * y^3 = 8x^6y^3.

Step 2: Now, we can simplify the entire expression by multiplying the terms outside the parentheses with the simplified term from step 1. We have:
(3x^0y^-4)(8x^6y^3) = 3 * 8 * x^0 * x^6 * y^-4 * y^3.

Step 3: Compute the coefficients and simplify the variables separately. The coefficient is 3 * 8 = 24. Now let's simplify the variables:
x^0 is equal to 1, so it can be removed from the expression.
x^6 * x^0 = x^6.
y^-4 * y^3 = y^(-4 + 3) = y^-1 = 1/y.

Putting it all together, we have:
(3x^0y^-4)(8x^6y^3) = 24x^6/y.

So the correct simplified expression is 24x^6/y.