Simplify Exponents and Radicals

Review and use the the rules for radicals and exponents to simplify exponents and radical expressions; questions with detailed solutions and explanations are presented along with their detailed solutions Try not to use the calculator to simplify numerical expressions except to check your answers. More questions on how to simplify radical expressions are included n this website.

Evaluate Numerical Expressions with Exponents

Question 1

Evaluate the following expressions:
  1.   32
  2.   - 34
  3.   (- 3)4
  4.   120
  5.   020
  6.   0- 4
  7.   (-1)7
  8.   (-1)4
  9.   (-1) - 3
  10.   (- 2 / 3) -2
  11.   (- 2)-2 / 4-2
  12.   - 3-3 + (- 2)-2
  13.   x4 for x = - 2
  14.   - x2 for x = - 3
  15.   - x5 for x = - 2
  16.   x4 for x = - 2 / 3
  17.   - x-2 for x = - 1 / 2
  18.   - x5 for x = - 1 / 3
detailed solutions

Evaluate Numerical Expressions with Radicals and rational exponents

Question 2

Evaluate the following expressions:
  1.   √(64)
  2.   ∛(-8)
  3.   43/2
  4.   82/3
  5.   0.00013/4
  6.   16- 3/4
  7.   √2 √8
  8.   ∛2 ∛(32)
  9.   √2 / √8
  10.   ∛(-16) / ∛2
  11.   - 2 (6√8) (56√8)
  12.   - 4 ∛(375) / (2∛3)
detailed solutions

Simplify Algebraic Expressions with Exponents

Question 3

Simplify the following expressions:
  1.   x2 x5
  2.   y4 / y2
  3.   (x2)-2

  4. \large {3(\dfrac{1}{2} x^4)(\dfrac{1}{3} x^3) }

  5. \large {(2 x)^4(\dfrac{1}{4} x^{-3}) }

  6. \large { \dfrac{(3x)^2(-2x)^3}{(2x)^2} }

  7. \large { \dfrac{(4x)^2(100 x)^0}{(3x)^2} }
  8.   (- 2 x2 y -3)3
  9.   (3 x2 y3) (2 x5 y - 2)
  10.   (- 2 x2 y3 z4) ( - 4 x3 y z - 8) ( 5 x y2 z2)

  11. \large { (-2xy^2)^2 \left (\dfrac{x^6}{(2x)^2} \right)^3 }

  12. \large { \left (\dfrac{4 x^6 y^3}{-8x^3y^{-2}} \right) }

  13. \large { \left (\dfrac{- 4 x^3 y^2}{3 x^3 y^3} \right) \left (\dfrac{3 x^2 y^5}{-6x^3y^2} \right) }

  14. \large { \dfrac{1}{6}(x^2 y z^3)\left (\dfrac{4 x^2 y^3}{3 x^2 y^{-3}z^2} \right) \left (\dfrac{3 x^2 y^5 z}{-x^3 y^2 z^3} \right) }

  15. \large { (4 x^{2/3})(-8x^{1/2}) }

  16. \large { (4 x)^{3/2}(9x)^{1/2} }

  17. \large { (- 27 x^{3/2})^{1/3} }

  18. \large {\left (\dfrac{-8x^3}{y^{-6}} \right)^{2/3} }

  19. \large { x^{5/3} x^{1/6} x ^{-11/6} }
detailed solutions

Simplify Algebraic Expressions with Radicals

Question 4


  1. \large { \sqrt{x^2} }

  2. \large { \sqrt[4]{16x^4} }

  3. \large { \sqrt{(2x - 1)^2} }

  4. \large { \sqrt[3]{-27x^3} }

  5. \large { \sqrt[3]{8 x^6 y^3} }

  6. \large { \sqrt{x^3} \sqrt{x^2} }

  7. \large { \sqrt[3]{\left (\dfrac{-8x^6}{y^{-3}} \right)} y}

  8. \large { \dfrac{ \sqrt[5]{64x^9 y^7}}{ \sqrt[5]{2 x^4 y^2}} }

  9. \large { (4\sqrt[8]{b^2})( 5\sqrt[8]{b^3})( \sqrt[8]{b^3}) }
detailed solutions

More References and links on quadratic functions and parabolas

the rules for radicals and exponents
simplify radical expressions
Divide Radical Expressions
Radical Expressions

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