Chapter 5

Simplify \(\frac{8 r^{3}}{4 \pi r^{2}}\)

Find the value of \(5(8+3)-2(-3-6)\).

In each case, simplify the given expression, if possible. \( x^{2}+3 x+1\)

Factorise (a) \(m n+11 m\), (b) \(3 p q-2 p\), (c) \(11 p q-3 q r\), (d) \(4 z x+20 y z\)

In the expression \(5^{4}\) state which number is the index and which is the base.

Remove the brackets from the given expression: \(7(2 x+y)\)

Remove the brackets from the given expression: \((-2)(a+b)\)

Simplify each of the following: (a) \(\frac{a^{11}}{a^{4}}\) (b) \(\left(a^{b}\right)^{4}\)

Simplify \(\frac{x+2}{x^{2}+3 x+2} .\)

In each case, simplify the given expression, if possible. \(\frac{1}{3} x+\frac{1}{2} x\)