1. Carry out the following divisions.
(i) \(28x^4 ÷ 56x\)

(ii) \(-36y^3 ÷ 9y^2\)

(iii) \(66pq^2r^3 ÷ 11qr^2\)

(iv) \(34x^3y^3z^3 ÷ 51xy^2z^3\)

(v) \(12a^8b^8 ÷ (-6a^6b^4)\)


Answer :

(i)Given:\(28x^4 ÷ 56x\)

\(=\frac{28\times x \times x \times x \times x}{28\times 2 \times x}\)

\(=\frac{x \times x \times x}2=\frac{x^3}2\)

(ii)Given:\(-36y^3 ÷ 9y^2\)

\(=\frac{-1\times 4 \times 9 \times y \times y \times y}{9\times y \times y}\)

\(=\frac{-1 \times 4 \times y}1=-4y\)

(iii)Given: \(66pq^2r^3 ÷ 11qr^2\)

\(=\frac{6\times 11 \times p \times q \times q \times r \times r \times r}{11\times q \times r \times r}\)

\(=\frac{6 \times p \times q \times r}1=6pqr\)

(iv)Given: \(34x^3y^3z^3 ÷ 51xy^2z^3\)

\(=\frac{6\times 11 \times x \times x \times x \times y \times y \times y \times z \times z \times z}{17\times 3 \times x \times y\times z \times z \times z}\)

\(=\frac{2 \times x \times x \times y}3=\frac{2x^2y}{3}\)

(v)Given:\(12a^8b^8 ÷ (-6a^6b^4)\)

\(=\frac{6\times 2 \times a \times a \times a \times a \times a \times a \times a \times a \times b \times b \times b \times b \times b \times b \times b \times b }{-1\times 6\times a \times a \times a \times a \times a \times a \times b \times b \times b \times b}\)

\(=\frac{2 \times a \times a \times b \times b \times b \times b}{-1}=-2a^2b^4\)

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