Questions: (7 x^7 y^8) / (5 a^7 b^8) ÷ (2 x^4 y^4) / (3 a^4 b^4)

Solution Steps

To solve the division of two fractions, we multiply the first fraction by the reciprocal of the second fraction. This involves flipping the numerator and the denominator of the second fraction and then multiplying the numerators together and the denominators together. After that, we simplify the resulting expression by combining like terms and reducing any common factors.

We start with the two fractions: \[ \frac{7 x^{7} y^{8}}{5 a^{7} b^{8}} \quad \text{and} \quad \frac{2 x^{4} y^{4}}{3 a^{4} b^{4}} \]

To divide the first fraction by the second, we multiply the first fraction by the reciprocal of the second: \[ \frac{7 x^{7} y^{8}}{5 a^{7} b^{8}} \div \frac{2 x^{4} y^{4}}{3 a^{4} b^{4}} = \frac{7 x^{7} y^{8}}{5 a^{7} b^{8}} \cdot \frac{3 a^{4} b^{4}}{2 x^{4} y^{4}} \]

Now we multiply the numerators and the denominators: \[ = \frac{7 \cdot 3 \cdot x^{7} \cdot y^{8}}{5 \cdot 2 \cdot a^{7} \cdot b^{8}} \cdot \frac{1}{x^{4} y^{4}} \cdot \frac{1}{1} \] This simplifies to: \[ = \frac{21 x^{3} y^{4}}{10 a^{3} b^{4}} \]

Final Answer