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!