Question

1)8x^2y^4*(-3x/4y^3) 2)-18x^2y^2/5ab:6xy^3/5a^2b^2 3)16a^2b^3:(-20a^5b^4/3x^2y) 4)-25x^4y^3/14m^2*(-21mn/10x^3y^2) 5)a^2-ab/b*b^2/a 6)ab+b^2/9*3a/b^2

Answer 1

$1) 8x^2y^4*(- \frac{3x}{4y^3} )=- 6x^3y$
$2) - \frac{18x^2y^2}{5ab} : \frac{6xy^3}{5a^2b^2}=- \frac{18x^2y^2*5a^2b^2}{5ab*6xy^3} = - \frac{3abx}{y}$
$3) 16a^2b^3:(- \frac{20a^5b^4}{3x^2y} )=- \frac{16a^2b^3*3x^2y}{20a^5b^4} =- \frac{12x^2y}{5a^3b}$
$4)- \frac{25x^4y^3}{14m^2} *(- \frac{21mn}{10x^3y^2} )=- \frac{25x^4y^3*21mn}{14m^2*10x^3y^2}=- \frac{15nxy}{4m}$
$5)a^2- \frac{ab}{b} * \frac{b^2}{a}= a^{2} - b^{2} =(a-b)*(a+b)$
$6)ab+ \frac{b^2}{9} * \frac{3a}{b^2} = \frac{a}{3} *(3b+1)$

Answer 2

To simplify the given expressions, let's break them down one by one:

1) 8x^2y^4*(-3x/4y^3) To simplify this expression, we can simplify the coefficients and combine the variables with the same base: = (8 * -3 * x^2 * x)/(4 * y^4 * y^3) = -24x^3/4y^7 = -6x^3/y^7

2) -18x^2y^2/5ab:6xy^3/5a^2b^2 To simplify this expression, we can multiply the numerator by the reciprocal of the denominator: = -18x^2y^2/5ab * 5a^2b^2/6xy^3 = (-18 * 5 * x^2 * y^2 * a^2 * b^2)/(5 * a * b * 6 * x * y^3) = -3x^2y^2a^2b/2xy^3 = -3x^(2-1)y^(2-3)a^(2-1)b^(1-1) = -3x/2y

3) 16a^2b^3/(-20a^5b^4/3x^2y) To simplify this expression, we can multiply the numerator by the reciprocal of the denominator: = 16a^2b^3 * 3x^2y/(-20a^5b^4) = (16 * 3 * a^2 * b^3 * x^2 * y)/(-20 * a^5 * b^4) = -24x^2y/a^3b

4) -25x^4y^3/14m^2*(-21mn/10x^3y^2) To simplify this expression, we can multiply the numerator by the reciprocal of the denominator: = -25x^4y^3 * 10x^3y^2/14m^2 * -21mn = (-25 * 10 * -21 * x^4 * x^3 * y^3 * y^2 * m * n)/(14 * m^2 * x^3 * y^2) = 5250x^(4+3-3)y^(3+2-2)m^(-2+1)n^1/14 = 375xn

5) a^2 - ab/b * b^2/a To simplify this expression, we can simplify each term separately and then combine them: = a^2 - (ab/b) * (b^2/a) = a^2 - (ab * (b^2/a)) / b = a^2 - (ab * b^2) / (ab) = a^2 - b = a^2 - b

6) ab + b^2/9 * 3a/b^2 To simplify this expression, we can simplify each term separately and then combine them: = ab + (b^2/9) * (3a/b^2) = ab + (3a * b^2) / (9 * b^2) = ab + (3a/b) = ab + 3a/b

These are the simplified expressions for the given equations.