reduce to lowest terms.
72r cubed s to fourth
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132r cubed s to the tenth
To reduce the given expression to its lowest terms, we need to simplify the numerator and the denominator separately.
Let's start with the numerator: 72r^3s^4
To simplify the numerator, we need to find the highest common factor (HCF) of the coefficients (72) and the variables (r^3 and s^4).
First, let's factorize 72:
72 = 2 * 2 * 2 * 3 * 3
Now, let's consider the variables.
The highest power of r that exists in the numerator is r^3, and the highest power of s is s^4.
So, the numerator can be written as:
72r^3s^4 = (2 * 2 * 2 * 3 * 3) * r^3 * s^4
Now, let's simplify the denominator: 132r^3s^10
Similarly, we need to find the HCF of the coefficients (132) and the variables (r^3 and s^10).
Let's factorize 132:
132 = 2 * 2 * 3 * 11
For the variables, the highest power of r is r^3, and the highest power of s is s^10.
So, the denominator can be written as:
132r^3s^10 = (2 * 2 * 3 * 11) * r^3 * s^10
Now, let's take a look at the simplified fraction:
(72r^3s^4) / (132r^3s^10)
To reduce it to its lowest terms, we can cancel out the common factors between the numerator and the denominator.
Canceling out the common factors (2, 3, r^3, and s^4), we get:
(2 * 2 * 3 * r^3 * s^4) / (2 * 2 * 3 * 11 * r^3 * s^10)
Simplifying further by canceling out the remaining r^3, we get:
(2 * 2 * s^4) / (2 * 2 * 3 * 11 * s^10)
Finally, we can cancel out the common factors (2 * 2) from the numerator and the denominator, which gives us:
s^4 / (3 * 11 * s^10)
Therefore, the expression is reduced to its lowest terms: s^4 / (33s^10)