Question

Divide:
(1) 4n⁴ ÷ n²
(2) 52m³ ÷ 13m
(3) 20c² ÷ 15c
(4) 36x⁵ ÷ 4x³
(5) 40a² ÷ (−10a)
(6) (−33y⁴) ÷ (−11y)

Answer 1

(1) 4n⁴ ÷ n²
Dividend = 4n⁴ = 2 × 2 × n × n × n × n
Divisor = n² = n × n
$\frac{4n^4}{n^2}=\frac{2\times 2\times n\times n\times n\times n}{n\times n}$
= 4n²
∴ 4n⁴ ÷ n² = 4n²

(2) 52m³ ÷ 13m
Dividend = 52m³ = 2 × 2 × 13 × m × m × m
Divisor = 13m = 13 × m
$\frac{52m^3}{13m}=\frac{2\times 2\times 13\times m\times m\times m}{13\times m}$
= 4m²
∴ 52m³ ÷ 13 m = 4m²

(3) 20c² ÷ 15c
Dividend = 20c² = 2 × 2 × 5 × c × c
Divisor = 15c = 3 × 5 × c
$$\begin{gathered} \frac{20c^2}{15c}=\frac{2\times 2\times 5\times c\times c}{3\times 5\times c} \\ =\frac{4c}{3} \end{gathered}$$
∴ 20c² ÷ 15c =$\frac{4c}{3}$

(4) 36x⁵ ÷ 4x³
Dividend = 36x⁵ = 2 × 2 × 3× 3 × x × x × x × x× x
Divisor = 4x³ = 2 × 2 × x × x × x
$\frac{36x^5}{4x^3}=\frac{2\times 2\times 3\times 3\times x\times x\times x\times x\times x}{2\times 2\times x\times x\times x}$
= 9x²
∴ 36x⁵ ÷ 4x³ = 9x²

(5)40a² ÷ (−10a)
Dividend = 40a² = 2× 2 × 2× 5 × a × a
Divisor = (−10a) = −2 × 5 × a
$\frac{40a^2}{-10a}=\frac{2\times 2\times 2\times 5\times a\times a}{-2\times 5\times a}$
= −4a

(6) −33y⁴; −11y i.e. −33y⁴÷ −11y
Dividend = −33y⁴ = − 3 × 11 × y × y × y × y
Divisor = −11y = − 11 × y
$\frac{-33y^4}{-11y}=\frac{-3\times 11\times y\times y\times y\times y}{-11\times y}$
= 3y³
∴ −33y⁴ ÷ −11y = 3y³