Question

simplify your answer as much as possible.

\\(16u^5 3w^{13}\\)

Explanation:

Identify the given expression

The image shows a multiplication of two algebraic fractions:

$$ \frac{5}{16u} \cdot \frac{13}{3w} $$

Our goal is to multiply these fractions and simplify the result as much as possible.

Multiply the numerators and denominators

To multiply fractions, we multiply the numerators together and the denominators together:

$$ \text{Numerator: } 5 \cdot 13 = 65 $$

$$ \text{Denominator: } 16u \cdot 3w = (16 \cdot 3) \cdot u \cdot w = 48uw $$

Combine into a single fraction

Write the product as a single algebraic fraction:

$$ \frac{65}{48uw} $$

Check for common factors to simplify

We examine the numerator \(65\) and the denominator coefficient \(48\) to see if they share any common factors:

• The prime factorization of \(65\) is \(5 \cdot 13\).
• The prime factorization of \(48\) is \(2^4 \cdot 3\).

Since they share no common prime factors, the fraction cannot be simplified further. The variables \(u\) and \(w\) are distinct and do not cancel.

Answer:

Simplify your answer as much as possible.
<blank>\(\frac{65}{48uw}\)</blank>