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Exponents, Roots and Scientific Notation on the GED Math Test

Exponents on the GED are a few rules used over and over: multiply powers with the same base and add the exponents, divide and subtract them, raise a power to a power and multiply them. Roots run the rules backward, and scientific notation is the same idea with a base of 10. The questions test which rule fits, and that is where marks go missing.

Updated September 21, 2026 · Lessons by Coach Crissy

Questions per set
10
Skills covered
6
Score-report category
Quantitative problem solving with rational numbers · 25% of the test

Exponents, roots and scientific notation: 10 questions

Questions
10
Timer
None
No calculator
None
  • Check each answer as you go and read the working before the next question.
  • New numbers every time, so a second run tests the skill rather than your memory.
  • The formula sheet and calculator sit in the toolbar, as they do on the real test.

No account or email needed.

GED Testing Service has said as much: a session by its senior math content specialist listed exponents and roots (Q.1.c and Q.2.c) among four knowledge gaps it sees in test-takers, alongside no-calculator items, and 3⁴ × 3² = 3⁶ is exactly the kind of question that can be asked before the calculator is switched on.

This site groups exponents with algebra because polynomial questions run on these rules, but officially Q.1.c, Q.2.b and Q.2.c sit in "quantitative problem solving with rational numbers", the 25% category shared with number operations, fractions, decimals, percents and ratios. Across four topics, that is perhaps two to four questions on a test of about 46, which is our arithmetic on the published weight rather than an official count. The rules also feed the 30% expressions-and-equations category, where multiplying binomials depends on them.

Skills in this set: Product, quotient and power rules for exponents · Simplifying and evaluating powers · Cubes and cube roots · Squares and square roots in context · Converting between standard and scientific notation · Comparing numbers in scientific notation

What the test asks

The Assessment Guide for Educators splits this topic across five indicators. Q.1.c is the exponent rules: rewriting a numeric expression with exponents, including fractional ones, in an equivalent form. Q.2.b covers squares and square roots, and Q.2.c cubes and cube roots, usually hidden in a square floor or a cube-shaped box. Q.2.d is recognizing an expression with no defined value, such as division by zero, and here that means the square root of a negative number. Scientific notation belongs to Q.2.e, real-life arithmetic problems.

The contexts stay ordinary: a county population of 3.6 × 10⁵ to write in standard form, a garden covering 225 square feet whose side you need, a crate holding 512 cubic inches whose edge you need, a science table with four measurements in mixed forms to put in order. Drop-down items can ask for a power and its value, and drag-and-drop items can ask you to sort values by size.

Expect some of this without the calculator. The test opens with about five questions taken before the on-screen TI-30XS is available, and an exponent rule fits there naturally, since the question tests the rule and the numbers keep the arithmetic light; our practice set marks the rule questions and notation conversions as no-calculator items. In the calculator section, the TI-30XS has keys for powers, square roots, cube roots and scientific notation, listed on the official calculator reference sheet.

The mistakes this set is built to catch

Each wrong answer in the practice set is the result of one specific slip, and the explanation names it. These are the ones that come up most in this topic.

1Mixing up the three rules

Multiplying powers with the same base adds the exponents: 3⁴ × 3² = 3⁶. Dividing subtracts them: 3⁴ ÷ 3² = 3². A power of a power multiplies them: (3⁴)² = 3⁸. The wrong answers swap these, so 3⁴ × 3² is offered as 3⁸ and as 9⁶, which also changed the base, and the base never changes. When in doubt, write the powers out and count the factors: six threes are 3⁶ however you group them.

2Reading a negative exponent as a negative number

5⁻² is not −25 and it is not −10. A negative exponent means a reciprocal, so 5⁻² = 1/5² = 1/25, a small positive number. The same confusion turns 8⁰ into 0 when it equals 1: 8³ ÷ 8³ leaves an exponent of 0, and any number divided by itself is 1. When a quotient hands you a negative or zero exponent, say what it means before you answer.

3Halving instead of taking a square root

A square garden covers 144 square feet, and the tempting answers for a side are 72 (half) and 36 (a quarter). Halving undoes doubling and dividing by 4 undoes multiplying by 4, but neither undoes squaring: the side is √144 = 12, because 12 × 12 = 144. A cube holding 343 cubic inches has an edge of 7, and dividing 343 by 3 will never find it. Check every root by multiplying it back out.

4Moving the decimal point the wrong way

Converting 0.00052 to scientific notation means moving the point four places right to reach 5.2, and because the number is smaller than 1 the exponent is negative: 5.2 × 10⁻⁴. The choices will include 5.2 × 10⁴ (wrong sign), 5.2 × 10⁻³ (one place short) and 52 × 10⁻⁵ (right value, wrong form, because the front number must be at least 1 and less than 10). Count the places, then check big or small before signing the exponent.

A worked example

A streaming company stores 8.4 × 10⁷ megabytes of video. Each of its servers holds 2 × 10⁴ megabytes. How many servers does the company need to hold all of the video?

  1. Set up the division

    How many servers means how many times 2 × 10⁴ fits into 8.4 × 10⁷: a division. Split it into front numbers and powers of ten, handled separately.

    (8.4 × 10⁷) ÷ (2 × 10⁴) = (8.4 ÷ 2) × (10⁷ ÷ 10⁴)

  2. Divide the front numbers

    This part is ordinary decimal arithmetic: half of 8.4 is 4.2.

    8.4 ÷ 2 = 4.2

  3. Subtract the exponents

    Dividing powers with the same base keeps the base and subtracts the exponents, so the result is 4.2 × 10³, already in proper form because 4.2 is between 1 and 10.

    10⁷ ÷ 10⁴ = 10⁷⁻⁴ = 10³

  4. Write it out and check

    A positive exponent of 3 moves the decimal point three places right, so 4.2 × 10³ is 4,200. Multiply back: 4,200 servers holding 20,000 megabytes each is 84,000,000 megabytes, which is 8.4 × 10⁷.

    4.2 × 10³ = 4,200; check: 4,200 × 20,000 = 84,000,000 = 8.4 × 10⁷

Answer: 4,200 servers

How to practice it

  1. When a rule will not come, write the powers out: 2⁵ × 2² is five twos times two more twos, seven twos in all, so the exponent is 7. A few seconds of writing rebuilds any rule and shows why the base stays put.
  2. Memorize the squares up to 15² = 225 and the cubes up to 6³ = 216. On no-calculator questions they turn √169 or ∛125 into an instant answer, and on calculator questions they let you sanity-check the screen. Put them on a card and run through it on the bus.
  3. For scientific notation, decide the sign before you count: a number bigger than 10 gets a positive exponent and a number smaller than 1 a negative one, so 0.0041 cannot be 4.1 × 10³. Then check that the front number is between 1 and 10, because 41 × 10⁻⁴ has the right value and the wrong form.
  4. Learn the calculator keys before test day. The TI-30XS has a square key, a power key, square-root and cube-root keys and a scientific-notation key, all shown on the official calculator reference sheet. Knowing them means a root question in the calculator section costs seconds rather than a minute of hunting.

Frequently asked questions

Are the exponent rules on the GED formula sheet?

No. The sheet covers area, perimeter, volume, surface area, mean and median, slope, the quadratic formula and the Pythagorean theorem, with no line for exponents or roots. The product, quotient and power rules, and what a zero or negative exponent means, have to come from memory.

Can I use the calculator for square roots and cube roots?

In the second part, yes: the on-screen TI-30XS has square-root and cube-root keys, and its power key handles any exponent. The first part, about five questions, is taken without the calculator, so the small perfect squares and cubes are worth knowing by heart.

Is scientific notation on the GED math test?

Yes. Indicator Q.2.e lists numbers in scientific notation among the real-life arithmetic problems the test can ask, and the calculator reference sheet covers the key for entering them. Expect conversions in both directions, comparisons of values in different forms, and the occasional division where the exponent rules do the work.

How many exponent questions are on the GED?

GED Testing Service does not publish a count per topic. Exponents, roots and scientific notation share the 25% rational-numbers category with three other topics, so on a test of about 46 questions a fair guess is two to four items; that is our arithmetic on the published weight. The official skill-gap session that named exponents and roots is reason enough to practice them even if the count is small.

Sources

Figures on this page were checked against these sources on the dates shown.

  1. Assessment Guide for Educators: Mathematical Reasoning · GED Testing Service · checked September 13, 2026
  2. Mathematics Formula Sheet (2026-02 revised) · GED Testing Service · checked September 13, 2026

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