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Common Core Standard HSN-RN.A.1 Questions

Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. For example, we define 51/3 to be the cube root of 5 because we want (51/3)3 = 5(1/3)3 to hold, so (51/3)3 must equal 5.

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Grade 9 Exponents
What is the reciprocal of [math]b^4?[/math]
  1. [math]1/b^4[/math]
  2. [math]b^(-4)[/math]
  3. [math]1/(b^(-4)[/math]
  4. [math]b^(1/4)[/math]
Grade 11 Exponents
Evaluate the expression [math]3^(x + 2) [/math] when [math]x = -2[/math].
  1. [math]1/3[/math]
  2. [math]1[/math]
  3. [math]3[/math]
  4. [math]81[/math]
Grade 10 Radicals CCSS: HSN-RN.A.2
What is [math]root3( 27/125)[/math] in simplest form?
  1. [math](3 root3 5)/5[/math]
  2. [math](3)/(root3 5)[/math]
  3. [math](root3 5)/5[/math]
  4. [math](3)/5[/math]
Grade 11 Exponents CCSS: HSN-RN.A.2
Simplify [math](4x^4y)^(3/2)[/math]. Assume all variables are positive.
  1. [math]4x^6y^(3/2)[/math]
  2. [math]8x^6y^(3/2)[/math]
  3. [math]4x^4y^(3/2)[/math]
  4. [math]2x^6y^(3/2)[/math]
Grade 9 Radicals CCSS: HSN-RN.A.2
What is [math]root3 20 * root3 6 [/math][math][/math] in simplest form?
  1. [math]root 3 120[/math]
  2. [math]2(root 2 15)[/math]
  3. [math]8(root 3 15)[/math]
  4. [math]2(root 3 15)[/math]
Grade 11 Exponents CCSS: HSN-RN.A.2
Simplify. [math](x^2y)/(x^(3/4)y^(1/3)[/math]
  1. [math]x^(5/4)y^(2/3)[/math]
  2. [math]x^(11/14)y^(4/3)[/math]
  3. [math]x^(3/2)y^(1/3)[/math]
  4. [math]x^(1/2)y^(1/3)[/math]
Grade 11 Nonlinear Equations and Functions
What is the solution of [math]5x^(2/3) - 7 = 13?[/math]
  1. [math]-4[/math]
  2. [math]+-4[/math]
  3. [math]+-8[/math]
  4. [math]20[/math]

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