Exponents and roots — SSAT Upper practice questions

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Practice 115 Exponents and roots questions in the app

What this topic is

Exponents and roots questions check whether you can apply the rules for powers without slipping.

Multiplying powers with the same base adds the exponents, raising a power to a power multiplies them, and a negative base raised to an odd power stays negative, so negative one-half cubed is negative one-eighth. Square roots undo squaring, and simplifying a root means pulling out perfect-square factors.

SSAT Upper items often ask which expression is not equal to a given power, so choices that look different may in fact be equivalent rewrites, as eight squared and four cubed both equal sixty-four. Rewriting every choice in the same base is the dependable approach.

Sample questions

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

Question 1Easier

Calculate: ${(- \frac{3}{2})}^{3}$

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Answer: B — $- \frac{27}{8}$

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

Question 2Easier

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

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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 $\frac{24 m^{3} n^{2}}{18 m n^{5}}$ .

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

✗ Not this one

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

✗ Not this one

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

✗ Not this one

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

✓ Correct

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

✗ Not this one

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Answer: D — $\frac{4 m^{2}}{3 n^{3}}$

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

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

Practice 115 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)