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MATHlove<33
Welcome to Mathlove.

This site was made by select students from 2I oF Colegio San Agustin, Makati (SY 07 - 08) for partial fulfillment of their Math requirements.

It contains lessons on Rational Exponents and an Introduction to Radicals.
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Exercises


Simplifying Exponential Expressions Involving Rational Exponents

EXERCISES:

 
  1. 49 ½
  2. 2m1/3
  3. 163/4
  4. 45/2
  5. 64-2/3
  6. (7x + 2)2/3
  7. 8-4/3
  8. 81/3
  9. (9x4)1/2
  10. 2x3/5

 

ANSWERS:
  1. 7
  2. 23vm
  3. 8
  4. 32
  5. 1/16
  6. 3v(7x + 2)2
  7. 1/16
  8. 2
  9. 3x2
  10. 25vx3

 

Extracting the Principal/Negative Root of a Radical Expression

EXERCISES:

 
  1. 4
  2. -49
  3. vX16
  4. 64
  5. 3v27
  6. 3v-1
  7. -v36
  8. v64Y20
  9. 3v1/8
  10. 3v-27X

 

ANSWERS:

 
  1. ± 2
  2. not a real number
  3. x8
  4. ± 8
  5. 3
  6. -1
  7. -6
  8. 8y10
  9. ½
  10. -3x3

 

 

 

Nth Root

 

EXERCISES:

 

  1. v9
  2. 3v-(1/8)
  3. 4v81
  4. - v25a4b6
  5. 3v27x9

 

ANSWERS:

 

1.       3

EXPLANATION: Since 3 squared is 9, 3 is the square root of 9. Note that we are only interested in the principal root and since 9 is positive and there is not a sign in front of the radical, our answer is positive 3. If there had been a negative sign in front of our radical, the answer would have been -3.

2.       -1/2

EXPLANATION: Since -1/2 cubed is -1/8, our answer is going to be -1/2.

3.       3

EXPLANATION: Since 3 raised to the 4th power is 81, our answer is going to be 3.

4.       -5a2b3

5.       3x3