Question

14с/49с а⁴b/ab³ 3a²b/9a³ 12a⁴b²/18a³b³ 25a³bc²/125ac³

Answer 1

$\displaystyle\bf\\1)\\\\\frac{14c}{49c} =\frac{7c\cdot 2}{7c\cdot 7} =\frac{2}{7} \\\\2)\\\\\frac{a^{4}b }{ab^{3} } =\frac{ab\cdot a^{3} }{ab\cdot b^{2} } =\frac{a^{3} }{b^{2} } \\\\4)\\\\\frac{12a^{4} b^{2} }{18a^{3} b^{3} }=\frac{6a^{3} b^{2} \cdot 2a}{6a^{3} b^{2} \cdot 3b}=\frac{2a}{3b} \\\\5)\\\\\frac{25a^{3}bc^{2} }{125ac^{3} } =\frac{25ac^{2} \cdot {a^ 2}b }{25ac^{2}\cdot 5c } =\frac{a^{2} b}{5c}\\\\3)\\\\\frac{3a^{2} b}{9a^{3} } =\frac{3a^{2} \cdot b}{3a^{2} \cdot 3a} =\frac{b}{3a}$

Answer 2

To simplify the given expressions, let's break down each term and reduce them to their simplest form:

1. $\frac{14c}{49c}$

   Both the numerator and denominator have a common factor of 7c, so you can simplify it as follows:

   $\frac{14c}{49c} = \frac{14}{49} \cdot \frac{c}{c} = \frac{14}{49} = \frac{2}{7}$.

2. $\frac{a^4b}{ab^3}$

   Here, we can simplify by canceling common factors between $a^4$ in the numerator and $ab^3$ in the denominator:

   $\frac{a^4b}{ab^3} = \frac{a^3}{b^2}$.

3. $\frac{3a^2b}{9a^3}$

   We can simplify this fraction by canceling a common factor of $3$ and $a^2$:

   $\frac{3a^2b}{9a^3} = \frac{a^2b}{3a^3}$.

4. $\frac{12a^4b^2}{18a^3b^3}$

   First, simplify the fraction by canceling common factors of $6$ in both the numerator and denominator:

   $\frac{12a^4b^2}{18a^3b^3} = \frac{2a^4b^2}{3a^3b^3}$.

5. $\frac{25a^3bc^2}{125ac^3}$

   Here, we can simplify by canceling common factors between $25$ in the numerator and $125$ in the denominator, as well as $a$ in the numerator and denominator, and $c^2$ in the numerator and $c^3$ in the denominator:

   $\frac{25a^3bc^2}{125ac^3} = \frac{a^2}{5c}$.

So, the simplified expressions are:

1. $\frac{2}{7}$
2. $\frac{a^3}{b^2}$
3. $\frac{a^2b}{3a^3}$
4. $\frac{2a^4b^2}{3a^3b^3}$
5. $\frac{a^2}{5c}$

Answer 3

It looks like you've provided a series of expressions with variables and exponents. I'll simplify each expression for you:

1. (14c / 49c): This can be simplified by canceling out common factors in the numerator and denominator: (14c / 49c) = (2/7)

2. (a⁴b / ab³): This can be simplified by canceling out common factors in the numerator and denominator: (a⁴b / ab³) = (a⁴ / a) = a³b

3. (3a²b / 9a³): This can be simplified by canceling out common factors in the numerator and denominator: (3a²b / 9a³) = (a²b / 3a³) = (1 / 3a)

4. (12a⁴b² / 18a³b³): This can be simplified by canceling out common factors in the numerator and denominator: (12a⁴b² / 18a³b³) = (2a⁴b² / 3a³b³) = (2a / 3b)

5. (25a³bc² / 125ac³): This can be simplified by canceling out common factors in the numerator and denominator: (25a³bc² / 125ac³) = (a³bc² / 5ac³) = (bc² / 5c²)

So, the simplified expressions are:

1. (14c / 49c) = (2/7)
2. (a⁴b / ab³) = a³b
3. (3a²b / 9a³) = (1 / 3a)
4. (12a⁴b² / 18a³b³) = (2a / 3b)
5. (25a³bc² / 125ac³) = (bc² / 5c²)