Chapter 5

Simplify $$ \frac{y^{6} y^{-3} y^{0.5}}{y^{-2} y^{7}} $$

Show that (a) \(\frac{n !}{(n-1) !}=n\), (b) \(\frac{(n+1) !}{(n-1) !}=n(n+1)\) (c) \(\frac{n !}{(n+1) !}=\frac{1}{n+1}\).

Write out explicitly \(\sum_{i-1}^{3} f_{i}\left(x_{i}-\bar{x}\right)^{2}\).

Write down the reciprocal of (a) 18 (b) \(\frac{1}{11}\) (c) \(\frac{3}{8}\) (d) \(\frac{2 x}{3 y}\)

(a) Express \(\frac{1}{u}+\frac{1}{v}\) as a single fraction. (b) Hence find the reciprocal of \(\frac{1}{u}+\frac{1}{v}\).

Remove the brackets from the given expression: \(\frac{3}{4}\left(\frac{1}{2} x+7\right)\)

Simplify (a) \(x^{2} x^{5} x^{9}\), (b) \(\frac{x^{9}}{x^{4}}\), (c) \(\frac{x^{4}}{x^{5}}\).

Express \(\frac{1}{s}+\frac{1}{s^{2}}\) as a single fraction.

If \(V=A h\) find the value of \(V\) when \(A=3\) and \(h=26\).

Express \(-\frac{6}{s+3}-\frac{4}{s+2}+\frac{3}{s+1}+2\) as a single fraction.