GMAT Tip

While it’s impossible to find the square root of negative numbers, it is possible to find the cube root of negative numbers.

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In the GMAT Powers and Roots module, you will learn all of the concepts, techniques and strategies needed to answer powers and rootsquestions on the GMAT. In particular, the GMAT Powers and Roots module covers the following topics:

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

 

GMAT POWERS AND ROOTS VIDEOS

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

Additional Practice

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 (2015 edition or 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

Official Guide for GMAT Quantitative Review (2nd edition)

Problem Solving: 36, 47, 55, 74, 86, 96, 97, 163, 170

Data Sufficiency: 31, 51, 54, 79, 81, 113
 

Track your progress by entering answers directly into our free, downloadable GMAT Prep Now Improvement Chart for the Official Guide (2015 edition or 13th edition)