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

37 questions on the paper
81 practice questions in the app
Free

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

What this topic is

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.

Sample questions

Pick an answer to see whether it is right — nothing is saved, and nothing needs an account.

Question 1Easier

Which expression has the greatest value?

2^5

✓ Correct

2^3 \cdot 3

✗ Not this one

4^2

✗ Not this one

2^4 + 2

✗ Not this one

Show answer

Answer: A — $2^5$

$2^5=32$ ; $2^3\cdot3=24$ ; $4^2=16$ ; $2^4+2=18$ . So $2^5$ has the greatest value.

Question 2Easier

$y=3^{x}$ , $t=3^{-x}$ , $x=-2$

Column A	Column B
The value of $y$	The value of $t$

The quantity in Column A is greater✗ Not this oneThe quantity in Column B is greater✓ CorrectThe two quantities are equal✗ Not this oneThe relationship cannot be determined from the information given✗ Not this one

Show answer

Answer: B — The quantity in Column B is greater

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

Question 3Easier

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

12✓ Correct26✗ Not this one

\sqrt{26}

✗ Not this one144✗ Not this one

Show answer

Answer: A — 12

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

Every question is picked for where you are right now, wrong answers come back until they stick, and it all works offline.

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

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

What this topic is

Sample questions

More ISEE Upper topics

Quantitative Reasoning