Questions: Find the quotient and simplify the result. [ frac2 x^55 x^6 div frac6 x10 x^4 ]

Solution Steps

To find the quotient and simplify the given expression, we first need to rewrite the division of fractions as multiplication by the reciprocal. Then, we simplify the resulting expression by canceling common factors in the numerator and the denominator. Finally, we simplify the expression by combining like terms.

We start with the expression: \[ \frac{2 x^{5}}{5 x^{6}} \div \frac{6 x}{10 x^{4}} \] This can be rewritten as: \[ \frac{2 x^{5}}{5 x^{6}} \times \frac{10 x^{4}}{6 x} \]

Now, we can simplify the expression: \[ \frac{2 \cdot 10 \cdot x^{5} \cdot x^{4}}{5 \cdot 6 \cdot x^{6} \cdot x} \] This simplifies to: \[ \frac{20 x^{9}}{30 x^{7}} \]

Next, we can cancel common factors in the numerator and the denominator: \[ \frac{20}{30} \cdot \frac{x^{9}}{x^{7}} = \frac{2}{3} \cdot x^{2} \]

Final Answer