Question

SCREENSHOT DOWN BELOW

Answer 1

THERE YA GO BUDDY!!

Explanation:

To simplify the expression (27xy)/(63yz), we can cancel out common factors in the numerator and denominator.

Let's break down each term into its prime factors:

27 = 3 * 3 * 3

63 = 3 * 3 * 7

x = x (no prime factors)

y = y (no prime factors)

z = z (no prime factors)

Now, let's simplify the expression:

(27xy)/(63yz) = (3 * 3 * 3 * x * y) / (3 * 3 * 7 * y * z)

We can cancel out the common factors of 3, y, and z:

(3 * 3 * 3 * x * y) / (3 * 3 * 7 * y * z) = (3 * 3 * x) / (3 * 7 * z)

Simplifying further:

(3 * 3 * x) / (3 * 7 * z) = 9x / 21z

Finally, we can simplify the fraction by dividing both the numerator and denominator by their greatest common factor, which is 3:

9x / 21z = 3x / 7z

Therefore, the simplified form of the expression (27xy)/(63yz) is 3x / 7z.

Answer 2

`(3x)/(7z)`

Explanation:

We can simplify the fraction:

`(27xy)/(63yz)`

by canceling common factors that appear in both the numerator and denominator.

First, we can see that there is a y in the numerator and denominator, so we can cancel both instances of that:

`(27x\!\!\\ot \!y)/(63\!\!\\ot \!yz)`

`= (27x)/(63z)`

Next, we can rewrite the constants with their prime factorizations: the simplest way of representing them as the multiplication of only prime numbers.

`= (3 \cdot 3 \cdot 3 \cdot x)/(3\cdot 3 \cdot 7 \cdot z)`

Now, we can see that the numerator and denominator share a common factor (3 · 3), so we can cancel that as well:

`(\\ot3\, \cdot \!\!\\ot3 \cdot 3 \cdot x)/(\\ot3\,\cdot \!\!\\ot3 \cdot 7 \cdot z)`

`= \boxed{(3x)/(7z)}`