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) \(12a^ 8b^ 8 = 2 × 2 × 3 × a ^8 × b ^8 \)

\(6a^ 6b^ 4 = 2 × 3 × a ^6 × b^ 4\)

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

=\(-2a^2b^4\)