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Radicals and Rational Exponents

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Radicals and Rational Exponents Answer Key

1. 
Simplify. [math]root3(27x^10)[/math]
  1. [math]27x^10[/math]
  2. [math]root3(27x^10)[/math]
  3. [math]3root3(x^10)[/math]
  4. [math](3x^3)root3x[/math]
2. 
If a field is [math]3 root(5)(x^8)[/math] units long and it is divided into [math]12 root(3)(x^4)[/math] segments, how long is each segment?
  1. [math]1/4 sqrt(x^4)[/math]
  2. [math]-9 root(2)(x^4)[/math]
  3. [math]1/4 root (15)(x^4)[/math]
  4. [math]1/4 root(5/3)(x^2)[/math]
3. 
Express the following expression in simplest radical form using only one radical sign.

[math]9^(1/2)*x^(3/2)*y^(5/4)[/math]
  • [math]3sqrt(x^3y^(5/2))[/math]
4. 
An oval is [math]1/2 root(5)(x^2y^3)[/math] meters long. If a Kara completes [math]5 root(3)(x^2y)[/math] laps, how many meters has she run? Give your answer in simplified radicals.
  1. [math]5/2x root(15)(xy^14)[/math]
  2. [math]5/2x root(3)(xy^14)[/math]
  3. [math]5 root(3)(xy^30)[/math]
  4. [math]2x root(15)(xy^14)[/math]
5. 
What is the ratio of [math]3 root(3)(x^2) sqrt(y^3)[/math] to [math]4 sqrt(x^3) root(3)(y^2)[/math] in the form __:1? Give your answer in the form of a radical.
  • [math](3 root(3)(x^2) sqrt(y^3))/(4 sqrt(x^3) root(3)(y^2)):1[/math]
    [math](3 x^(2/3)y^(3/2))/(4x^(3/2)y^(2/3)):1[/math]
    [math]3/4 x^(-5/6)y^(5/6):1[/math]
    [math](3y^(5/6))/(4x^(5/6)):1[/math]
    [math](3root(6)(y^5))/(4root(6)(x^5)):1[/math]
6. 
Write the ratio of [math]4 root(3)(x^4)[/math] to [math]2sqrt(x^5)[/math] in the form __:1. Show all of your work.
  • [math](4 root(3)(x^4))/(2sqrtx^5)[/math]
    [math](4x^(4/3))/(2x^(5/2)[/math]
    [math]2x^(-7/6)[/math]
    [math]2/(root(6)(x^7)):1[/math]
7. 
Express each of the following with fractional exponents.

a. [math]root3(25^2)[/math]


b. [math]sqrt35[/math]
  • [math]25^(2/3)[/math]
    [math]35^(1/2)[/math]
8. 
If a field is [math]5 root(3)(x^2)[/math] units long and it is divided into [math]10 root(4)(x^5)[/math] segments, how long is each segment?
  • [math](5x^(2/3))/(10x^(5/4)) = 1/2 x^(-7/12) = 1/(2x^(7/12))[/math]
9. 
Express the following expression in simplest radical form using only one radical sign.
[math]27^(1/3)*x^(4/5)*y^(2/5)*z^(1/5)[/math]
  • [math]3root5(x^4y^2z)[/math]
10. 
Simplify.

[math](16x^4)^(3/2)[/math]
  1. [math]64x^6[/math]
  2. [math]4x^6[/math]
  3. [math]64x^10[/math]
  4. [math]4x^10[/math]

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