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. x²x³
2. x³x ^{− 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. x⁵x ^{− 5}
11. x¹4y ^{− 7}

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

17. $\frac{2}{\sqrt{4}}$
18. $\frac{8}{4 + \sqrt{26}}$
19. $\frac{12}{12 - \sqrt{76}}$
20. $\frac{3}{3 - \sqrt{65}}$
21. $\frac{9}{9 + \sqrt{9}}$