Question

4m^3/35a^3b^2•(-14a^2b/6m)

Answer 1

- 4*m³*14*a²*b / (35*a³*b²*6m)=

- (4/15)*m² / (a*b)= - 4m²/(15ab)  -  это ответ.

Answer 2

To simplify the expression $\frac{4m^3}{35a^3b^2} \cdot (-\frac{14a^2b}{6m})$, you can follow these steps:

Step 1: Simplify each fraction separately.

For the first fraction $\frac{4m^3}{35a^3b^2}$, you can't simplify it further because there are no common factors in the numerator and denominator.

For the second fraction $-\frac{14a^2b}{6m}$, you can simplify it by canceling common factors. The greatest common factor of 14, 6, and $m$ is 2. The greatest common factor of $a^2$ and $a$ is $a$, and the greatest common factor of $b$ and $b$ is $b$. So, you can simplify it as follows:

$-\frac{14a^2b}{6m} = -\frac{2 \cdot 7 \cdot a \cdot a \cdot b}{2 \cdot 3 \cdot m} = -\frac{7a^2b}{3m}$

Step 2: Multiply the simplified fractions together.

Now, you can multiply the two simplified fractions:

$\frac{4m^3}{35a^3b^2} \cdot (-\frac{7a^2b}{3m})$

Step 3: Cancel common factors.

You can cancel common factors between the numerators and denominators:

$= \frac{4 \cdot \cancel{m^3}}{35 \cdot a^3 \cdot b^2} \cdot (-\frac{7 \cdot a^2 \cdot \cancel{b}}{3 \cdot \cancel{m}})$

$= \frac{4}{35a^3} \cdot (-\frac{7a^2}{3})$

Step 4: Multiply the remaining terms together.

Now, simply multiply the fractions together:

$= \frac{4}{35a^3} \cdot (-\frac{7a^2}{3}) = -\frac{28a^2}{105a^3}$

So, the simplified expression is $-\frac{28a^2}{105a^3}$.