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

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What this topic is

Negative exponents are the first stumbling block in Exponents, roots, and scientific notation.

A negative exponent means a reciprocal, not a negative number: two to the power of negative three equals one-eighth. Roots can be multiplied under one radical, so the square root of two times the square root of eight is the square root of sixteen, which is four. Questions may ask which of several expressions has the greatest value, or compare a power with its reciprocal in a quantitative comparison.

Scientific notation appears when very large or very small numbers must be compared, and the exponent on ten decides most of that comparison.

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 — $2^{5}$

$2^{5} = 32$ ; $2^{3} \cdot 3 = 24$ ; $4^{2} = 16$ ; $2^{4} + 2 = 18$ . 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 $x = - 2$ , $y = 3^{- 2} = \frac{1}{9}$ , 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 82 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