Exponents and Radicals

Here you will find a concise collection of exponents and radicals practice problems. Visit this page directly at hunkim.com/exponents

1. 3^3
   Solution
   27
2. 2^{10}
   Solution
   1024
3. (-3)^3
   Solution
   -27
4. (-2)^4
   Solution
   16
5. 1^{123}
   Solution
   1
6. 1^0
   Solution
   1
7. 1^{2.5+\pi \sqrt{5}}
   Solution
   1
8. 0^1
   Solution
   0
9. 0^0
   Solution
   Undefined
10. (-1)^{101}
    Solution
    -1
11. -(-1)^{10}
    Solution
    -1
12. \left (\frac{5}{3}\right)^2
    Solution
    25/9
13. \left( \frac{5}{3}\right)^{-2}
    Solution
    9/25
14. (p^3)(p^2)\times p
    Solution
    p^6
15. (x^2)^3
    Solution
    x^6
16. (2a^2b^3)^3
    Solution
    8a^6 b^9
17. \frac{9x^4y^4}{3xy^2}
    Solution
    3x^3 y^2
18. \frac{x}{x^{-4}}
    Solution
    x^5
19. \left( \frac{4pq^6}{2p^3q^3}\right)^3
20. Solution
    \frac{8q^9}{p^6}
21. \left( \frac{a}{b^3}\right)^{-2}
    Solution
    \frac{b^6}{a^2}
22. Solve \frac{3^{10}}{3^x}=3^6
    Solution
    4
23. Solve \left( \frac{2^{1-2x}}{2^{x+3}}\right)^3=4
    Solution
    -8/9
24. Write \frac{15^6}{3^6} as a single power
    Solution
    15625
25. Solve 2^{x+1}=8^{3-2x}
    Solution
    8/7
26. Simplify -\frac{8x^5-12x^3}{6x^3}
    Solution
    2-\frac{4}{3} x^2
27. Express x^{1/2} as a radical
28. Solution
    \sqrt{x}
29. Express \sqrt[3]{x} as a fractional exponent
    Solution
    x^{1/3}
30. Write x^{2/5} as a radical
    Solution
    \sqrt[5]{x^2}
31. Evaluate \sqrt{\frac{9}{25}}
    Solution
    \frac{3}{5}
32. Write \sqrt{8} as a mixed radical
    Solution
    2\sqrt{2}
33. Write \sqrt[3]{81} as a mixed radical
    Solution
    3\sqrt[3]{3}
34. Write 3\sqrt{2} as an entire radical
    Solution
    \sqrt{18}
35. Write 2\sqrt[3]{3} as an entire radical
    Solution
    \sqrt[3]{24}
36. Simplify \sqrt{2}\times \sqrt{5}+\left( \sqrt[3]{2}\right) \left( \sqrt[3]{5}\right)
    Solution
    \sqrt{10}+\sqrt[3]{10}
37. Simplify \frac{\sqrt{125}}{5}
    Solution
    \sqrt{5}
38. (0.09)^{1/2}
    Solution
    0.3
39. (0.000008)^{1/3}
    Solution
    0.02
40. Solve \sqrt{ \sqrt[3]{ \sqrt{x}} }=2
    Solution
    4096
41. Rationalize:
    1. \frac{1}{\sqrt{2}}
       Solution
       \sqrt{2}/2
    2. \frac{3}{\sqrt{3}}
       Solution
       \sqrt{3}/3
    3. \frac{2}{\sqrt[3]{2}}
       Solution
       \sqrt[3]{4}
42. Challenge:
    1. Challenge:\frac{(0.6x^{-1})^{-2}}{\left( \frac{2}{x}\right)^3}
       Solution
       \frac{25x^5}{72}
    2. Solve 9\times 27+2(3)^x=3^{x+1}
       Solution
       5
    3. Show that \sqrt[c]{a^b}=\left( \sqrt[c]{a}\right)^b
       Solution
       LS=\left( a^b \right)^{\frac{1}{c}}=a^{\frac{b}{c}}
       RS=\left( a^{\frac{1}{c}} \right)^b=a^{\frac{b}{c}}=LS
       
    4. Solve 9\times 27+2(3)^x=3^{x+1}
       Solution
       5
    5. Solve 4^{1.5x}=2(32^{x-1})
       Solution
       2
    6. Solve x^{2/3}=5
       Solution
       5^{\frac{3}{2}}=5\sqrt{5}

---