Questions: [ frac12 b^45 c^3 d^3 div frac3 a b^310 c^2 d ]

Solution Steps

To simplify the given expression, we need to divide the two fractions. When dividing fractions, we multiply by the reciprocal of the divisor. This involves flipping the second fraction and then multiplying the numerators together and the denominators together.

We start with the expression: \[ \frac{\frac{12 b^{4}}{5 c^{3} d^{3}}}{\frac{3 a b^{3}}{10 c^{2} d}} \]

To simplify, we multiply by the reciprocal of the denominator: \[ \frac{12 b^{4}}{5 c^{3} d^{3}} \times \frac{10 c^{2} d}{3 a b^{3}} \]

Now, we can simplify the expression by multiplying the numerators and the denominators: \[ = \frac{12 \cdot 10 \cdot b^{4} \cdot d}{5 \cdot 3 \cdot a \cdot b^{3} \cdot c^{3} \cdot c^{2} \cdot d^{3}} \] This simplifies to: \[ = \frac{120 b^{4} d}{15 a b^{3} c^{5} d^{3}} \]

Now, we can reduce the coefficients and the variables: \[ = \frac{8 b}{a c d^{2}} \]

Final Answer