Simplify the Expression: (27yx/3x²)·(5y⁴x²/3y) Step-by-Step

To solve this problem, we'll follow these steps:

• Step 1: Simplify each fraction separately.
• Step 2: Multiply the simplified fractions together.
• Step 3: Cancel common terms if necessary.
• Step 4: Apply exponent rules for a clearer expression.

Step 1: Simplify each fraction:

The first fraction is $\frac{27yx}{3x^2}$. This can be simplified as follows:

$\frac{27yx}{3x^2} = \frac{27}{3} \cdot \frac{yx}{x^2} = 9 \cdot \frac{y}{x}$.

The second fraction is $\frac{5y^4x^2}{3y}$. Simplifying it, we have:

$\frac{5y^4x^2}{3y} = \frac{5x^2}{3} \cdot y^{4-1} = \frac{5x^2}{3} \cdot y^3$.

Step 2: Multiply the simplified fractions:

$9 \cdot \frac{y}{x} \times \frac{5x^2}{3} \cdot y^3 = \frac{9 \cdot 5x^2 \cdot y \cdot y^3}{3 \cdot x}$.

Step 3: Simplify again by cancelling out common terms:

$= \frac{9 \times 5 \cdot x \cdot y^{1+3}}{3} = \frac{45xy^4}{3}$.

Divide 45 by 3: $= 15xy^4$.

Therefore, the product of the two expressions simplifies to $15y^4x$, which matches choice 1.