In this module, you'll learn all of the concepts, techniques and strategies needed to answer powers and roots questions on the GRE. In particular, this module covers:

 Exponent laws Exponential growth Negative exponents Fractional exponents Units digits of large powers Equations with exponents Square roots and other roots “Fixing” the denominator

### Two ways to prepare

NOTE: Beneath most of the video lessons below, you’ll find a Reinforcement Activities box containing practice questions that are specifically related to the concepts covered in that lesson (e.g., the lesson on exponent laws). With this lesson format, you have two study options:

• Watch the video lesson first and then reinforce your learning by answering several related questions, or…
• Tackle the practice questions first and watch the lesson only if you need help with the concepts the practice questions test

For more on this learning strategy, read the “How to Beat the GRE” section of our course overview page.

## GRE POWERS AND ROOTS VIDEOS

• 1. Lesson: Introduction to Exponents (9:23)
• 2. Question: Big Exponents (1:32)
• 3. Lesson: Exponential Growth (2:57)
• 4. Question: 0.999 to the Power of k (1:28)
• 5. Lesson: Squaring Numbers Ending in 5 (2:22)
• 6. Lesson: Exponent Laws - Part I (7:07)
• 7. Question: Powers of 8 (1:12)
• 8. Question: Crazy Exponents (2:15)
• 9. Lesson: Negative Exponents (5:20)
• 10. Question: Floating Decimals (1:30)
• 11. Question: All Sorts of Rules (2:18)
• 12. Lesson: Exponent Laws - Part II (6:08)
• 13. Question: Simplify Fraction with Powers (2:13)
• 14. Lesson: Units Digit of Large Powers (3:28)
• 15. Question: Units Digit of 53 to Power of 35 (3:51)
• 16. Lesson: Introduction to Square Roots (6:25)
• 17. Question: Conclusion Based on Root (1:16)
• 18. Lesson: Other Roots (5:37)
• 19. Question: Ordering Powers of -0.5 (1:35)
• 20. Lesson: Properties of Roots (2:51)
• 21. Lesson: Simplifying Roots (6:16)
• 22. Lesson: Operations with Roots (3:53)
• 23. Question: Roots and Squares (1:26)
• 24. Question: Quotient with Cube Roots (1:02)
• 25. Lesson: Fractional Exponents (3:32)
• 26. Question: Bit of Everything (1:06)
• 27. Lesson: Solving Equations with Exponents (4:36)
• 28. Question: Variables in Base and Exponent (2:10)
• 29. Lesson: “Fixing” the Denominator (6:39)
• 30. Question: Root in the Denominator (1:58)
• 31. Question: Product of 2 Negative Powers (1:06)
• 32. Question: Cube Root of a Decimal (0:52)
• 33. Question: Negative Decimal Exponent (0:48)
• 34. Question: Equation with Powers of 11 (1:35)
• 35. Question: Fraction with Products of Powers (1:45)
• 36. Question: 2.5 to the kth Power (1:10)
• 37. Question: Units Digit of a Large Product (1:27)
• 38. Question: 2 and 3 with Exponent 7 (1:06)
• 39. Question: The 4th Power (0:57)
• 40. Question: Powers of 4 (1:08)
• 41. Question: 32 and 27 with Exponents (1:48)
• 42. Question: x with Powers of a, b and c (2:19)
• 43. Question: Power of 5 (1:42)
Total viewing time for the GRE Powers and Roots module: 121 minutes.

## Practice from Official Guide

Practice the skills and GRE-specific strategies you learned in this module by answering the following questions from the Official Guide to the GRE (3rd edition):

• 126(1), 128(4), 161(6), 166(3), 166(6), 261(5)

Here are the related questions in the Official Guide to the GRE (1st or 2nd edition):

• 121(1), 123(4), 151(6), 156(3), 156(6)

Note: The above practice questions are listed in the form page#(question#). So, for example, 121(1) represents question #1 on page 121.