A-level Mathematics/OCR/C1/Indices and Surds/Problems

Feel free to add more problems as long as you provide the solutions

Indices
Simplify the Indices.
 * 1) $$x^2x^3$$
 * 2) $$x^3x^{-2}$$
 * 3) $$\frac{x^5}{x^2}$$
 * 4) $$x^{-4}$$
 * 5) $$\left(x^3\right)^4$$
 * 6) $$\left(xy\right)^2$$
 * 7) $$\left(\frac{y}{b}\right)^3$$
 * 8) $$x^{\frac{2}{3}}$$
 * 9) $$\frac{x^2x^4}{\left(x^2\right)^2}$$
 * 10) $$x^5x^{-5}$$

Surds
Simplify the following Surds.
 * 1) $$\sqrt{9}$$
 * 2) $$\sqrt{25}$$
 * 3) $$\sqrt{45}$$
 * 4) $$\sqrt{63}$$
 * 5) $$\sqrt{100}$$
 * 6) $$\sqrt{48}$$
 * 7) $$\sqrt{98}$$
 * 8) $$\sqrt{75}$$
 * 9) $$\sqrt{32}$$
 * 10) $$\sqrt{320}$$
 * 11) $$\sqrt{256}$$
 * 12) $$\sqrt{\frac{9}{36}}$$
 * 13) $$\sqrt[3]{\frac{27}{125}}$$
 * 14) $$\sqrt{\frac{162}{200}}$$
 * 15) $$\sqrt{\frac{75}{3}}$$
 * 16) $$\sqrt{\frac{112}{72}}$$

Rationalize the Denominator


 * 1) $$\frac{2}{\sqrt{4}}$$
 * 2) $$\frac{8}{4 + \sqrt{26}}$$
 * 3) $$\frac{12}{12 - \sqrt{76}}$$
 * 4) $$\frac{3}{3 - \sqrt{65}}$$
 * 5) $$\frac{9}{9 + \sqrt{9}}$$
 * 6) $$\frac{a^2}{a+\sqrt{a}}$$

Indices and Surds/Problems