91Ó°ÊÓ

Multiplying fractions might sound tricky, but it's actually quite simple when broken down. To multiply two fractions, you just:

• Multiply the numerators together.
• Multiply the denominators together.

Remember, the numerator is the top part of the fraction, and the denominator is the bottom part. When multiplying fractions, there's no need to find a common denominator like you do when adding or subtracting fractions.
Instead, just multiply across as shown in the exercise: \[\frac{5}{2} \times \frac{4}{15} = \frac{5 \times 4}{2 \times 15}\] This simplifies to: \[\frac{20}{30}\] Did you notice that simplifying fractions can often be easier if you simplify the fractions before multiplying? By reducing any common factors, you can considerably simplify the steps needed in your calculations.
This is a powerful technique to keep in mind every time you multiply fractions!

Exponents represent repeated multiplication. For instance, \(x^7\) means multiplying \(x\) by itself seven times. When dealing with exponents, especially in algebraic terms, understanding the basic rules can simplify your work significantly.
Here are a few crucial exponent rules involved in the exercise:

• Product of Powers Rule: When multiplying two bases that are the same, add their exponents. For example, \(x^a \times x^b = x^{a+b}\).
• Quotient of Powers Rule: When dividing like bases, subtract the exponents: \(x^a \div x^b = x^{a-b}\).

In our given problem, when simplifying \(\frac{5x^7}{2x^5}\), you use the Quotient of Powers Rule: \[x^{7-5} = x^2\] Similarly, simplifying \(\frac{4x^3}{15x}\) yields:\[x^{3-1} = x^2\] This understanding is not just theoretical; it has practical applications in simplifying expressions and solving equations efficiently."},{