Question

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(b) simplify \\(\frac{10x^2}{y} \div \frac{2y^3}{x^2y}\\).

Explanation:

Convert division to multiplication

To divide by a fraction, we multiply by its reciprocal. We flip the second fraction upside down:

$$ \frac{10x^2}{y} \div \frac{2y^3}{x^2 y} = \frac{10x^2}{y} \times \frac{x^2 y}{2y^3} $$

Combine into a single fraction

We multiply the numerators together and the denominators together:

$$ \frac{10x^2 \cdot x^2 y}{y \cdot 2y^3} = \frac{10x^4 y}{2y^4} $$

Simplify the coefficients and variables

We divide the numerical coefficients and subtract the exponents of the common variables:

• For the coefficients: \(\frac{10}{2} = 5\)
• For the variable \(y\): \(\frac{y}{y^4} = \frac{1}{y^3}\)
• The term \(x^4\) remains in the numerator.

Combining these gives:

$$ \frac{5x^4}{y^3} $$

Answer:

$$\frac{5x^4}{y^3}$$