Posted by Jessie on Monday, October 18, 2010 at 3:48pm. I think I figured it out-please check

I'm really stuck on these problems-
Simplify 6xy(3xy)^-2? I think this is 2/3xy
choices were
2/xy
3xy
2xy
2/3xy

Simplify 12xyz^-2/8x^-2z
choices were 3x^2y/2z^3
3x^3y/z^3
3x^3y/2z^3
x^3/2z^3

I think it is 3x^3y/2z^3

Thank you for checking

Thank you

1. Correct, assuming it is 2/(3xy)

2. Correct, assuming it is 3x³y/(2z³)

Thank you

You're welcome!

To simplify the expression 6xy(3xy)^-2, you need to use the exponent rules. The negative exponent in (3xy)^-2 means that you need to move the base with the negative exponent (3xy) to the denominator and change the sign of the exponent. So, the expression becomes 6xy/(3xy)^2.

To simplify further, you can calculate the square of 3xy. The square of a quantity is found by multiplying the quantity by itself. Thus, (3xy)^2 = 9x^2y^2.

Now, substitute this value back into the expression: 6xy/9x^2y^2. Since there is a common factor of xy in the numerator and denominator, you can cancel them out. This leaves you with 6/9x^2y or 2/3x^2y.

Therefore, the correct answer is 2/3x^2y.

For the second expression 12xyz^-2/8x^-2z, you can use the exponent and division rules to simplify it.

First, let's simplify the expression in the denominator, x^-2. The negative exponent means that you have to move the base x^-2 to the denominator and change the sign of the exponent, making it 1/x^2.

Now, substitute this simplified denominator back into the expression: 12xyz^-2/8 * 1/x^2 * z.

Simplify further: (12 * y * z) / (8 * x^2 * x).

Next, simplify the numbers in the numerator and denominator: 12/8 reduces to 3/2, and x^2 * x is equal to x^3.

Finally, putting all the simplified terms together, we have 3/2 * y * z / x^3.

Therefore, the correct answer is 3x^3y/2z^3.

You were correct in both your answers! Well done!