Question

1) 14m^4c/n^6 × n^5/35mc^6 2) 36x^3/y^2 : (9x6y) 3) 8m + 8n/ a^3 × 5a^10/m^2-n^2 4) 3x -15/x+4 : x^2 -25/3x+12 * ^ - степень

Answer 1

Ответ:

Объяснение:

$1)~~ \dfrac{14m^4c}{n^6} \cdot \dfrac{n^5}{35mc^6} = \dfrac{2m^3}{5nc^5}$

$2)~~ \dfrac{36x^3}{y^2} : 9x^6y = \dfrac{36x^3}{y^2} \cdot \dfrac{1}{9x^6y} =\dfrac{4}{x^3y^3}$

$3)~~\dfrac{8m+8n}{a^3} \cdot \dfrac{5a^{10}}{m^2 - n^2} = \dfrac{8(m+n)}{a^3} \cdot \dfrac{5a^{10}}{(m - n)(m+n)}=\dfrac{40a^7}{m-n}$

$4)~~ \dfrac{3x - 15}{x+4} : \dfrac{x^2-25}{3x+12}= \dfrac{3(x - 5)}{x+4} \cdot \dfrac{3(x+4)}{{(x-5)(x+5)}}=\dfrac{9}{x+5}$

Answer 2

Let's simplify each of the given expressions:

1. $\frac{14m^4c}{n^6} \times \frac{n^5}{35mc^6}$

To multiply fractions, we can multiply the numerators together and the denominators together: $\frac{14m^4c \cdot n^5}{n^6 \cdot 35mc^6}$

Now, simplify the expression: $\frac{14m^4c \cdot n^5}{35mn^6c^6}$

The final simplified expression is $\frac{2m^3n^5}{5n^6c^5}$

2. $\frac{36x^3}{y^2} : \frac{9x^6y}{1}$

To divide fractions, we can multiply the first fraction by the reciprocal of the second fraction: $\frac{36x^3}{y^2} \times \frac{1}{\frac{9x^6y}{1}}$

Simplify the expression: $\frac{36x^3}{y^2} \times \frac{1}{\frac{9x^6y}{1}} = \frac{36x^3}{y^2} \times \frac{1}{9x^6y}$

Next, cancel out any common factors between the numerator and denominator: $\frac{4x^{-3}}{y}$

The final simplified expression is $\frac{4}{x^3y}$

3. $8m + \frac{8n}{a^3} \times \frac{5a^{10}}{m^2-n^2}$

Let's simplify each part separately: $8m + \frac{8n}{a^3} = 8m + \frac{8n}{a^3}$ (no simplification possible)

Next, simplify the second part: $\frac{5a^{10}}{m^2-n^2}$

To factor the denominator, we can use the difference of squares: $m^2-n^2 = (m+n)(m-n)$

Therefore: $\frac{5a^{10}}{m^2-n^2} = \frac{5a^{10}}{(m+n)(m-n)}$

The final simplified expression is $8m + \frac{8n}{a^3} \times \frac{5a^{10}}{(m+n)(m-n)}$

4. $\frac{3x - 15}{x+4} : \frac{x^2 - 25}{3x+12}$