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

 Exponent laws Negative exponents Fractional exponents Equations with exponents Square roots and other roots “Fixing” the denominator

### Two ways to prepare

Beneath each video lesson in this module, we have a Related Resource box with practice questions that test the concepts covered in the video. With this lesson format, you have two learning 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

## GMAT POWERS AND ROOTS VIDEOS

• 1. Lesson: Introduction to Exponents (9:23)
• 2. Lesson: Exponential Growth (2:57)
• 3. Question: Big Exponents (1:05)
• 4. Lesson: Squaring Numbers Ending in 5 (2:22)
• 5. Lesson: Exponent Laws - Part I (7:07)
• 6. Question: Powers of 8 (1:12)
• 7. Question: Is this fraction less than 1? (3:32)
• 8. Lesson: Negative Exponents (5:20)
• 9. Lesson: Exponent Laws - Part II (6:08)
• 10. Question: Simplify Fraction with Powers (2:13)
• 11. Lesson: Units Digit of Large Powers (3:28)
• 12. Question: Units Digit of 53 to Power of 35 (3:51)
• 13. Lesson: Introduction to Square Roots (6:12)
• 14. Question: Root x Squared (1:53)
• 15. Lesson: Other Roots (5:37)
• 16. Question: The Powers of -0.5 (1:35)
• 17. Lesson: Properties of Roots (2:51)
• 18. Lesson: Simplifying Roots (6:16)
• 19. Lesson: Operations with Roots (3:53)
• 20. Question: Simplification with Cube Roots (1:02)
• 21. Lesson: Fractional Exponents (3:32)
• 22. Question: Bit of Everything (1:06)
• 23. Lesson: Solving Equations with Exponents (4:36)
• 24. Lesson: “Fixing” the Denominator (6:39)
• 25. Question: Root in the Denominator (1:58)
• 26. Question: Does the Power Equal 1? (1:38)
• 27. Question: Cube Root of a Decimal (0:52)
• 28. Question: Negative Decimal Exponent (0:48)
• 29. Question: Equation with Powers of 11 (1:35)
• 30. Question: x to the 7th Power (1:38)
• 31. Question: Last Digit of a Large Product (1:27)
• 32. Question: 2 and 3 with Exponent 7 (1:06)
• 33. Question: Equivalent Powers (2:34)
• 34. Question: Powers of 4 (1:08)
• 35. Question: x with Powers of a, b and c (2:19)
• 36. Question: Power of 5 (1:42)
Total viewing time for the GMAT Powers and Roots module: 113 minutes.

NOTE: In each of the above video lessons, you’ll find a Related Resources box containing several practice questions that are specifically related to the concepts covered in that lesson (e.g., the lesson on square roots). Conversely, the practice questions below cover a variety of topics under the umbrella of GMAT Powers and Roots, and are intended for general reinforcement.

Given this, you may find it beneficial to work on the questions below after you’ve mastered the module content by watching the video lessons and answering concept-specific practice questions from the Related Resources boxes. For more on this learning strategy, visit our course overview page.

Problem Solving (level of difficulty: 350 to 500)

Product of primes  (powers)

Ordering values  (powers, fractions)

Problem Solving (level of difficulty: 500 to 650)

M = sum of various roots (roots)

k to the power of one-third  (roots,  powers)

Which one is negative?  (powers)

Possible orderings   (powers, inequalities)

Roots and powers  (roots, powers)

Problem Solving (level of difficulty: 650 to 800)

12 to the power of n  (powers, integer properties)

Powers of 5 and 2  (powers, algebra)

Equation with powers of 5  (powers, algebra)

Musical scale  (powers, roots)

Data Sufficiency (level of difficulty: 350 to 500)

Roots of squares and vice versa  (powers, roots)

Data Sufficiency (level of difficulty: 500 to 650)

5 to the kth power  (powers, inequalities)

nth root of n  (roots)

Data Sufficiency (level of difficulty: 650 to 800)

Variable a raised to the power of a  (powers, integer properties)

a% of b% of c   (powers, percent, integer properties)

Variable exponents  (powers)

## Practice from the Official Guides

Official Guide for GMAT Review (2017 edition)

Problem Solving: 10, 28, 58, 77, 87, 95, 118, 128, 145, 164, 178, 185, 196, 198, 204, 208, 223

Data Sufficiency: 240, 243, 249, 255, 277, 327, 356, 361

Official Guide for GMAT Review (2016 edition)

Problem Solving: 7, 52, 57, 67, 78, 85, 105, 123, 128, 146, 163, 171, 183, 184, 188, 193, 204, 221

Data Sufficiency: 11, 20, 41, 112, 117, 163, 164, 170, 173

Official Guide for GMAT Review (2015/13th edition)

Problem Solving: 9, 35, 52, 65, 100, 106, 111, 122, 146, 163, 170, 176,  180, 196, 217, 227

Data Sufficiency: 15, 52, 101, 157, 159, 169, 172

While answering practice questions from the Official Guide for GMAT Review (2017, 2016 or 2015), you can enter your responses directly into our downloadable Improvement Chart. This will help track your progress and identify areas of weakness.