Share/Like This Page

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.

You can create printable tests and worksheets from these questions on Common Core standard HSN-RN.A.1! Select one or more questions using the checkboxes above each question. Then click the add selected questions to a test button before moving to another page.

Grade 9 Exponents CCSS: HSN-RN.A.1
Which of the following correctly explains why (610)6=10 ? Choose all correct answers.
  1. The 6's cancel out, leaving just 10.
  2. 610 can be rewritten as 1016, and then exponent laws can be applied (namely, (1016)6=1066=101=10).
  3. If the left hand side is rewritten as 6106, then the radical can be distributed to the 10 and the 6, and the rounded answer is about 10.
  4. The 6th root of 10 is asking for the number that, if multiplied by itself 6 times, would equal 10. Therefore, this number raised to the power of 6, is equal to 10.
Grade 9 Exponents CCSS: HSN-RN.A.1
Starting with the variable x, raise x to the power of 4. Which of the following represents an inverse operation? Choose all correct answers.
  1. Dividing the expression by 4.
  2. Taking the base-4 logarithm of the expression.
  3. Taking the 4th root.
  4. Raising the entire expression to the power of 1/4.
Grade 9 Exponents CCSS: HSN-RN.A.1
Grade 9 Exponents CCSS: HSN-RN.A.1
Which of the following is a correct way to rewrite the expression 4-53 ? Choose all that apply.
  1. 34-5
  2. -345
  3. 1345
  4. (34)-5
Grade 9 Exponents CCSS: HSN-RN.A.1
Which of the following is a reason why, when dealing with an equation or expression, one would switch from using radical notation (square roots, cube roots, etc), to rational exponents? Choose all correct answers.
  1. One can use exponent laws to simplify the expression or equation. For example, 3x6x9 becomes x63x92=x2+92=x42+92=x132.
  2. It avoids the issue of complex numbers. For example, -2 is complex, namely 2i where i is the square root of -1, but changing this into a rational exponent, -212, it is no longer complex.
  3. For an expression or equation with division, once the radical has been converted to a rational exponent, the factors can be more easily divided. For example, 8x744x3 becomes 8x724x34=2x72-34=2x144-34=2x114.
  4. Using rational exponents can lead to easier forms for evaluation. For example, 346 can be written as 463=42, which can then be easily evaluated.
Grade 9 Exponents CCSS: HSN-RN.A.1
Grade 9 Exponents CCSS: HSN-RN.A.1

Become a Pro subscriber to access Common Core questions

Unlimited premium printables Unlimited online testing Unlimited custom tests

Learn More About Benefits and Options