Exponents and roots — SSAT Upper practice questions

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.

Section: Quantitative (Math) 50 questions on the paper
108 practice questions in the app

Sample questions

Question 1

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

A $-\dfrac{27}{6}$
B $-\dfrac{27}{8}$
C $-\dfrac{9}{8}$
D $\dfrac{9}{8}$
E $\dfrac{27}{8}$

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 2

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

A $8^{2}$
B $2^{2} \times 2^{3}$
C $4^{3}$
D $2^{3} \times 2^{3}$
E64

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 3

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

A $\dfrac{4m^{2}n^{3}}{3}$
B $\dfrac{4m^{4}}{3n^{7}}$
C $\dfrac{4n^{3}}{3m^{2}}$
D $\dfrac{4m^{2}}{3n^{3}}$
E $\dfrac{3m^{2}}{4n^{3}}$

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

Practice 108 Exponents and roots questions in the app

Exponents and roots — SSAT Upper practice questions

Sample questions

More SSAT Upper topics

Quantitative (Math)