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Quantitative ReasoningFree

Exponents, roots, and scientific notation — ISEE Upper practice questions

On the ISEE Upper Quantitative Reasoning section, Exponents, roots, and scientific notation covers integer and negative powers, products of square roots, and numbers written in scientific form. A student has to evaluate and simplify expressions, compare their sizes, and convert among equivalent writings. Items often present several powered or radical expressions and ask which is largest, or they give paired exponential definitions and a negative input and ask for a value. Choices tend to be near-miss numbers or rewritten forms, with traps around the sign of an exponent, combining radicals incorrectly, and moving the decimal the wrong way.

  • Section: Quantitative Reasoning 37 questions on the paper
  • 81 practice questions in the app

Sample questions

Question 1

Which expression has the greatest value?

  1. A252^5
  2. B23⋅32^3 \cdot 3
  3. C424^2
  4. D24+22^4 + 2
Show answer

Answer: A — 252^5

25=322^5=32; 23⋅3=242^3\cdot3=24; 42=164^2=16; 24+2=182^4+2=18. So 252^5 has the greatest value.

Question 2

y=3xy=3^{x}, t=3−xt=3^{-x}, x=−2x=-2

Column AColumn B
The value of yyThe value of tt
  1. AThe quantity in Column A is greater
  2. BThe quantity in Column B is greater
  3. CThe two quantities are equal
  4. DThe relationship cannot be determined from the information given
Show answer

Answer: B — The quantity in Column B is greater

Since x=−2x=-2, y=3−2=19y=3^{-2}=\dfrac{1}{9}, while t=32=9t=3^{2}=9. Thus y<ty<t.

Question 3

What is the value of 8⋅18\sqrt{8}\cdot\sqrt{18}?

  1. A12
  2. B26
  3. C26\sqrt{26}
  4. D144
Show answer

Answer: A — 12

8⋅18=144=12\sqrt{8}\cdot\sqrt{18}=\sqrt{144}=12.

Practice 81 Exponents, roots, and scientific notation questions in the app

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