Study on the fly SSAT Upper Quantitative (Math)Exponents and roots

Quantitative (Math)

Exponents and roots — SSAT Upper practice questions

50 questions on the paper
111 practice questions in the app
Free

Practice 111 Exponents and roots questions in the app

What this topic is

Exponents and roots on the SSAT Upper Quantitative (Math) section covers powers, roots, and the rules used to rewrite or evaluate them.

A student has to recognize equivalent exponential forms, simplify variable expressions that include powers, and compute a value such as a negative fraction raised to the third power while keeping the correct sign. Items often ask which choice is not equivalent to a power such as 2^6, or to simplify or calculate a short expression.

Choices tend to be integers or rewritten powers and roots, with traps such as swapping base and exponent or dropping a negative on an odd power.

Sample questions

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

Question 1Easier

Calculate: $\left(-\dfrac{3}{2}\right)^{3}$

-\dfrac{27}{6}

✗ Not this one

-\dfrac{27}{8}

✓ Correct

-\dfrac{9}{8}

✗ Not this one

\dfrac{9}{8}

✗ Not this one

\dfrac{27}{8}

✗ Not this one

Show answer

Answer: B — $-\dfrac{27}{8}$

$\left(-\dfrac{3}{2}\right)^{3} = -\dfrac{27}{8}$ . Cube the numerator and denominator, and keep the negative sign for an odd power.

Question 2Easier

Which of the following is NOT equivalent to $2^{6}$ ?

8^{2}

✗ Not this one

2^{2} \times 2^{3}

✓ Correct

4^{3}

✗ Not this one

2^{3} \times 2^{3}

✗ Not this one64✗ Not this one

Show answer

Answer: B — $2^{2} \times 2^{3}$

$2^{6} = 64$ . Also $4^{3} = 64$ , $8^{2} = 64$ , and $2^{3} \times 2^{3} = 2^{6} = 64$ . But $2^{2} \times 2^{3} = 2^{5} = 32$ , which is not equivalent.

Question 3Easier

Simplify the variable expression $\dfrac{24m^{3}n^{2}}{18mn^{5}}$ .

\dfrac{4m^{2}n^{3}}{3}

✗ Not this one

\dfrac{4m^{4}}{3n^{7}}

✗ Not this one

\dfrac{4n^{3}}{3m^{2}}

✗ Not this one

\dfrac{4m^{2}}{3n^{3}}

✓ Correct

\dfrac{3m^{2}}{4n^{3}}

✗ Not this one

Show answer

Answer: D — $\dfrac{4m^{2}}{3n^{3}}$

Coefficients simplify to $\dfrac{24}{18} = \dfrac{4}{3}$ . For variables, $m^{3-1} = m^{2}$ and $n^{2-5} = n^{-3}$ , so the result is $\dfrac{4m^{2}}{3n^{3}}$ .

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

Practice 111 Exponents and roots questions in the app

Exponents and roots — SSAT Upper practice questions

What this topic is

Sample questions

More SSAT Upper topics

Quantitative (Math)