Examples -> Algebra -> Exponents -> Powers

 Exercise 1. [ID:84] [Level: ] [Number of helps: 0] [Number of pictures: 0] [Number of steps: 4] [Number of characters: 0] Evaluate the following expression:$\frac{{a}^{2}-4}{a-2}$
 Exercise 2. [ID:117] [Level: ] [Number of helps: 0] [Number of pictures: 0] [Number of steps: 5] [Number of characters: 0] Evaluate the following expression:$\frac{{2}^{-2}·{5}^{3}·{10}^{-4}}{{2}^{-3}·{5}^{2}·{10}^{-5}}$
 Exercise 3. [ID:119] [Level: ] [Number of helps: 0] [Number of pictures: 0] [Number of steps: 6] [Number of characters: 0] Evaluate the following expression:$\frac{2{a}^{2}}{5{b}^{-2}}÷\frac{10{a}^{-3}}{6{b}^{-1}}$
 Exercise 4. [ID:120] [Level: ] [Number of helps: 0] [Number of pictures: 0] [Number of steps: 8] [Number of characters: 0] Evaluate the following expression:${\left(6-4{\left(\frac{5}{16}\right)}^{0}\right)}^{-2}+{\left(\frac{2}{3}\right)}^{-1}-\frac{3}{4}$
 Exercise 5. [ID:121] [Level: ] [Number of helps: 0] [Number of pictures: 0] [Number of steps: 7] [Number of characters: 0] Evaluate the following expression:${a}^{-n}{\left({a}^{n}-1\right)}^{-1}-2{\left({a}^{2n}-1\right)}^{-1}+{a}^{-n}{\left({a}^{n}+1\right)}^{-1}$
 Exercise 6. [ID:124] [Level: ] [Number of helps: 1] [Number of pictures: 0] [Number of steps: 8] [Number of characters: 0] Evaluate the following expression:$\frac{{a}^{n}-{a}^{-n}}{{a}^{n}+{a}^{-n}+2}$
 Exercise 7. [ID:125] [Level: ] [Number of helps: 0] [Number of pictures: 0] [Number of steps: 10] [Number of characters: 0] Evaluate the following expression:${\left(\frac{{x}^{-1}+{y}^{-1}}{y{x}^{-1}+x{y}^{-1}}\right)}^{-1}+{\left(\frac{{x}^{-1}+{y}^{-1}}{2}\right)}^{-1}-\frac{{x}^{-1}-{y}^{-1}}{{x}^{-1}·{y}^{-1}}$
 Exercise 8. [ID:134] [Level: ] [Number of helps: 0] [Number of pictures: 0] [Number of steps: 11] [Number of characters: 0] Evaluate the following expression:${\left(\frac{{2}^{x}+{2}^{-x}}{2}\right)}^{2}-{\left(\frac{{2}^{x}-{2}^{-x}}{2}\right)}^{2}$
 Exercise 9. [ID:259] [Level: ] [Number of helps: 0] [Number of pictures: 0] [Number of steps: 10] [Number of characters: 0] Evaluate the following expression:$\frac{\frac{1}{x}-64}{4+\frac{2}{x}+\frac{1}{{x}^{2}}}·\frac{{x}^{2}}{4-\frac{4}{x}+\frac{1}{{x}^{2}}}-\frac{4{x}^{2}\left(2x+1\right)}{1-2x}x\in Z$
 Exercise 10. [ID:275] [Level: ] [Number of helps: 0] [Number of pictures: 0] [Number of steps: 9] [Number of characters: 0]
 Exercise 11. [ID:276] [Level: ] [Number of helps: 0] [Number of pictures: 0] [Number of steps: 11] [Number of characters: 0] Simplify the following expression:$\frac{\frac{5{a}^{-x}+5}{{a}^{-2x}-{a}^{-x}+1}}{\frac{1}{{a}^{-x}+1}+\frac{3{a}^{-x}}{{a}^{3x}+1}}$