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
To simplify 6xy(3xy)^-2, we need to apply the exponent to the term inside the parentheses first. The exponent -2 means that we need to take the reciprocal of the term and square it. Thus, (3xy)^-2 becomes 1/(3xy)^2 = 1/(3^2 * x^2 * y^2) = 1/(9x^2y^2).
Now, we can multiply this term by 6xy. Multiplication of terms means we can multiply the numerators and the denominators together. So, 6xy * 1/(9x^2y^2) = (6xy)/(9x^2y^2).
To simplify further, we can divide both the numerator and the denominator by the common factors. In this case, we can divide both 6 and 9 by 3, and both x and y by xy. Doing this, we get:
(6xy)/(9x^2y^2) = (2xy)/(3x^2y^2) = 2/(3xy).
Therefore, the simplified form of 6xy(3xy)^-2 is 2/(3xy).
For the second problem, simplifying 12xyz^-2/8x^-2z, we need to apply the negative exponent first. The negative exponent -2 tells us to take the reciprocal and square the term. So, z^-2 becomes 1/z^2.
Next, we can simplify the numerical values by dividing both 12 and 8 by 4, giving us:
(12xyz^-2)/(8x^-2z) = (3xy)/(2x^-2z^3).
Now, let's simplify the x term. When dividing x terms, we subtract the exponents since we're dealing with negative exponents. So, x^-2 divided by x is equal to x^-2-1 = x^-3 = 1/x^3.
With this simplification, we get:
(3xy)/(2x^-2z^3) = (3xy)/(2 * 1/x^3 * z^3) = (3xy * x^3)/(2z^3) = 3x^3y/(2z^3).
Thus, the simplified form of 12xyz^-2/8x^-2z is 3x^3y/(2z^3).
You got both answers correct! Great job!
To simplify the expression 6xy(3xy)^-2, you can use the power rule, which states that (a^m)^n is equal to a^(m*n). In this case, (3xy)^-2 means that you need to multiply the exponents -2 and 3xy.
So, (3xy)^-2 = 3^-2 * (xy)^-2
= 1/3^2 * (xy)^-2
= 1/9 * (xy)^-2
= 1/9 * x^-2 * y^-2
= 1/9 * (1/x^2) * (1/y^2)
= 1/9 * 1/(x^2 * y^2)
= 1/(9 * x^2 * y^2)
Now, you can multiply this result by 6xy:
6xy * 1/(9 * x^2 * y^2)
= (6xy)/(9 * x^2 * y^2)
= (2 * 3 * x * y * 1)/(3 * 3 * x * x * y * y)
= (2/3) * (1/(x * x)) * (1/(y * y))
= 2/3xy
So, you were correct, the simplified form is indeed 2/3xy.
Similarly, to simplify the expression 12xyz^-2/8x^-2z, you can use the division and power rules.
12xyz^-2/8x^-2z
= (12/8) * (xyz^-2)/(x^-2z)
= 3/2 * (xy/(x^2z^3))
= 3x^1 * y^1 * (1/(2z^3))
= 3x * y * 1/(2z^3)
= 3xy/(2z^3)
So, you were correct again, the simplified form is indeed 3xy/(2z^3).
Good job!