The simplest form of:
(2). 4a³/bc² ÷ 2a/bc is 2a²/c
(4). 6x²y/3y ÷ 2xy is x/y
(6). (2x²/3 × 6/x) ÷ 8x²/25 is 25/2x
(8). (y² - 8y + 7)/10y² ÷ (y - 7)/5y is (y - 1)/2
When simplifying two fractions that are to be divided, the division sign can become multiplication interchanging the divisor fraction that is is a/b ÷ c/d becomes a/b × d/c.
(2). 4a³/bc² ÷ 2a/bc = 4a³/bc² × bc/2a
cancelling out the common factors we have;
4a³/bc² ÷ 2a/bc = 2a²/c × 1/1
4a³/bc² ÷ 2a/bc = 2a²/c
(4). 6x²y/3y ÷ 2xy = 6x²y/3y × 1/2xy
6x²y/3y ÷ 2xy = x/y × 1/1
6x²y/3y ÷ 2xy = x/y
(6). (2x²/3 × 6/x) ÷ 8x²/25 = (2x²/3 × 6/x) × 25/8x²
(2x²/3 × 6/x) ÷ 8x²/25 = 2x²/3 × 6/x × 25/8x²
(2x²/3 × 6/x) ÷ 8x²/25 = 1/1 × 1/1 × 25/x
(2x²/3 × 6/x) ÷ 8x²/25 = 25/x
(8). (y² - 8y + 7)/10y² ÷ (y - 7)/5y = (8). (y² - 8y + 7)/10y² ÷ (y - 7)/5y = (8). (y² - 8y + 7)/10y² × 5y/(y - 7)
(y² - 8y + 7)/10y² ÷ (y - 7)/5y = (y - 1)(y - 7)/10y² × 5y/(y - 7).
(y² - 8y + 7)/10y² ÷ (y - 7)/5y = (y - 1)/2y × 1/1
(y² - 8y + 7)/10y² ÷ (y - 7)/5y = (y - 1)/2y
Therefore, the expressions in simplest form are 2a²/c, x/y, 25/x and (y - 1)/2y respectively for 4a³/bc² ÷ 2a/bc, 6x²y/3y ÷ 2xy, (2x²/3 × 6/x) ÷ 8x²/25 and (y² - 8y + 7)/10y² ÷ (y - 7)/5y.