What is the result when the algebraic fraction 4X²/Y is multiplied by Y²/8X?

To find the result of multiplying the algebraic fractions ( \frac{4X^2}{Y} ) and ( \frac{Y^2}{8X} ), we start by applying the rule for multiplying fractions, which is to multiply the numerators together and the denominators together.

The numerator of the first fraction is ( 4X^2 ) and the numerator of the second fraction is ( Y^2 ). When we multiply these, we get:

[

4X^2 \times Y^2 = 4X^2Y^2

]

Next, we look at the denominators. The denominator of the first fraction is ( Y ) and the denominator of the second fraction is ( 8X ). When we multiply these together, we have:

[

Y \times 8X = 8XY

]

Now we can combine both results into a single fraction:

[

\frac{4X^2Y^2}{8XY}

]

To simplify this fraction, we can factor out common terms. In the numerator, ( 4X^2Y^2 ) can be rewritten as ( 4X \cdot X \cdot