Exponents and scientific notation — SHSAT practice questions

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Practice 113 Exponents and scientific notation questions in the app

What this topic is

Exponent rules work only when the bases match: multiplying powers of the same base adds the exponents, dividing subtracts them, and raising a power to a power multiplies them.

A frequent error is multiplying exponents when they should simply be added. Scientific notation writes a number as a value of at least one and less than ten times a power of ten, so a product sometimes needs adjusting after multiplying.

Questions on exponents and scientific notation ask for a simplified value, a product in scientific notation, or the greatest of several listed values; comparing the powers of ten first sorts most of them.

Sample questions

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

Question 1Easier

What is $(4.0 \times 1 0^{5}) (3.0 \times 1 0^{- 2})$ in scientific notation?

1.2 \times 1 0^{3}

✗ Not this one

7.0 \times 1 0^{3}

✗ Not this one

1.2 \times 1 0^{4}

✓ Correct

1.2 \times 1 0^{7}

✗ Not this one

Show answer

Answer: C — $1.2 \times 1 0^{4}$

Multiply coefficients and add exponents: $4.0 \times 3.0 = 12.0$ and $5 + (- 2) = 3$ , so $12.0 \times 1 0^{3} = 1.2 \times 1 0^{4}$ .

Question 2Easier

What is $\frac{2^{5} \cdot 2^{3}}{2^{4}}$ ?

4✗ Not this one8✗ Not this one16✓ Correct32✗ Not this one

Show answer

Answer: C — 16

Combining exponents gives $2^{5 + 3 - 4} = 2^{4} = 16$ .

Question 3Easier

Four engineering tolerances are listed in scientific notation. Which listed value is greatest?

1.4 \times 1 0^{5}

✓ Correct

6.2 \times 1 0^{4}

✗ Not this one

8.9 \times 1 0^{3}

✗ Not this one

9.5 \times 1 0^{2}

✗ Not this one

Show answer

Answer: A — $1.4 \times 1 0^{5}$

Compare powers of 10 first. The greatest exponent dominates here, so $1.4 \times 1 0^{5}$ is largest.

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

Practice 113 Exponents and scientific notation questions in the app

Exponents and scientific notation — SHSAT practice questions

What this topic is

Sample questions

More SHSAT topics

Mathematics