Question

Carry out the following divisions. 

1. $28x^ 4 ÷ 56x$ 
2.  $–36y^ 3 ÷ 9y ^2$ 
3.  $66pq^2 r^ 3 ÷ 11qr^2$
4.  $34x^ 3y^ 3 z^ 3 ÷ 51xy^2 z^ 3$
5.  $12a ^8b^ 8 ÷ (– 6a^ 6b ^4 )$

Answer 1

(i) $28x^ 4 = 2 \times 2 \times 7 \times x \times x \times x × x$

$56x = 2 \times 2 \times 2 \times 7 \times x$

$\frac{28x^4}{56x} = \frac{2\times2\times7\times x\times x\times x\times x}{2\times2\times2\times7\times x}$

$=\frac{x^3}{2}=\frac{1}{2}x^3$

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(ii) $36y ^3 = 2 × 2 × 3 × 3 × y × y × y$

$9y^ 2 = 3 × 3 × y × y$

$\frac{-36y^3}{9y^2}=-\frac{2×2×3×3×y×y×y}{3×3×y×y=-4y}$

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$66 pq^2 r^ 3 = 2 × 3 × 11 × p × q × q × r × r × r$

$11qr^2 = 11 × q × r × r$

$\frac{66oq^2r^3}{11qr^2}=\frac{2×3×11×p×q×q×r×r×r}{11×q×r×r}=6pqr$

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(iv) $34 x^ 3 y^ 3 z^ 3 = 2 × 17 × x × x × x × y × y × y × z × z × z$

$51 xy^2 z^ 3 = 3 ×17 × x × y × y ×z × z × z$

$\frac{34x^3y^3z^3}{51xy^2z^3}=\frac{ 2×17×x×x×x×y×y×y×z×z×z}{3×17×x×y×y×z×z×z}$

=$\frac{2}{3}x^2y$

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(v) $12a^ 8b^ 8 = 2 × 2 × 3 × a ^8 × b ^8$

$6a^ 6b^ 4 = 2 × 3 × a ^6 × b^ 4$

$\frac{12a^8b^8}{(-6a^6b^4)}=\frac{2×2×3×a^8×b^8}{-2×3×a^6×b^4}$

=$-2a^2b^4$