I'm a little uneasy about this one, so I thought I'd ask someone who knows -
[QUOTE]
(5z^3w/-6m^3)*(-6m^5/25z^9)
(OR)
5z^3 -6m^5
------ * --------
-6m^3 25z^9
Perform the Operations and Simplify[/QUOTE]
It's a Multiple Choice.
a)wm^2/5z^5
b)wm^2/5z^6
c)z^3wm^5/5z^9m^3
d)none of the above
I chose (D) because the way I did my math I came up m having a power of 8. I feel like I'm wrong here.
My solution: (1/5)m^8wz^12
You forgot the w in your "OR" version. Your answer is wrong in any case. The ratio of the powers of m results in m^2.
The correct answer is (b)
To simplify the expression (5z^3w/-6m^3) * (-6m^5/25z^9), we can follow these steps:
Step 1: Group the terms with the same base together and simplify each term separately.
In the numerator, we have 5z^3w. In the denominator, we have -6m^3.
In the second fraction, we have -6m^5 in the numerator and 25z^9 in the denominator.
Step 2: Simplify the terms.
Let's first simplify the numerator of the first fraction: 5z^3w can be left as it is since there are no like terms to combine.
Next, let's simplify the denominator of the first fraction: -6m^3 can also be left as it is.
Similarly, in the second fraction, the numerator -6m^5 can be left as it is, and the denominator 25z^9 can also be left as it is.
Step 3: Combine the two fractions by multiplying.
Now we can multiply the simplified fractions:
5z^3w/-6m^3 * -6m^5/25z^9
When multiplying fractions, we multiply the numerators together and the denominators together:
(5z^3w * -6m^5) / (-6m^3 * 25z^9)
Step 4: Simplify further.
Multiply the numerator: 5 * -6 = -30, z^3 * w * m^5 = z^3wm^5.
Multiply the denominator: -6 * 25 = -150, m^3 * z^9 = (m^3)(z^9).
So, our expression becomes:
-30z^3wm^5 / -150m^3z^9
Step 5: Cancel out common factors.
We can cancel out the common factors between the numerator and denominator to simplify further:
-30z^3wm^5 / -150m^3z^9
= (1/5)(m^5/m^3)(w/z^6)
Simplifying the powers of m:
= (1/5) * m^(5-3) * (w/z^6)
= (1/5) * m^2 * (w/z^6)
= mw / 5z^6
So, the simplified expression is mw / 5z^6.
Comparing this answer to the multiple-choice options, the correct answer is (b) wm^2/5z^6.