If exponents look like a mess of tiny floating numbers, that’s a normal first reaction.
Think of a phone chain. You call 2 people, each of them calls 2 more, and each of those calls 2 more. That third round is 2 × 2 × 2 = 8 calls, and an exponent writes it short: 2³.
The catch? Wrong answers on the test are built from mixing up three rules. The fix is to check each rule by writing the numbers out the long way, which takes a few seconds.
On this page you’ll get:
- 25 practice questions (scroll up), new ones every time
- The 3 exponent rules, with examples you can check yourself
- Square roots and cube roots you can do in your head
- Scientific notation, explained with real numbers
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 GED exponent questions look like
The settings are ordinary: a county population of 3.6 × 10⁵ to write out in full, a square garden of 225 square feet whose side you need, a crate of 512 cubic inches whose edge you need. Some items ask you to sort values written in different forms from smallest to largest.
Rule 1, multiplying: add the exponents. 3⁴ × 3² = 3⁶. Check it yourself: that’s four threes times two more threes, six threes in all.
Rule 2, dividing: subtract the exponents. 3⁴ ÷ 3² = 3². Check it: 3⁴ is 81 and 3² is 9, and 81 ÷ 9 = 9, which is 3².
Rule 3, a power of a power: multiply the exponents. (3⁴)² = 3⁸. Check it: that’s 3⁴ times 3⁴, so four threes plus four more threes, eight in all.
A square root runs a square backward. A square garden of 225 square feet has sides of 15 feet, because 15 × 15 = 225. A cube root does the same for a box: a crate of 512 cubic inches has edges of 8 inches, because 8 × 8 × 8 = 512. Learn the common squares and cubes by heart, and these become head math.
One odd case: the square root of a negative number has no value in regular numbers, because any number times itself comes out positive. The test may ask you to spot that.
Scientific notation is how you write huge or tiny numbers without all the zeros, like the distance to the sun. The power of 10 tells you how far to move the decimal point. A county of 3.6 × 10⁵ people is 3.6 with the point moved 5 places right: 360,000. A tiny number like 0.00052 is 5.2 × 10⁻⁴, and the exponent is negative because the number is smaller than 1.
A rule question like 3⁴ × 3² fits the first five or so questions, which you answer without a calculator. After that, the on-screen TI-30XS has keys for powers, square roots, cube roots and scientific notation.
How many questions? There’s no official count per topic. GED Testing Service’s senior math content specialist has named exponents and roots as one of four skill gaps it sees in test-takers, and the topic shares the numbers-and-percents area of the test (about 25%) with number operations, fractions and ratios. Our estimate is two to four questions out of about 46.
The topics and area weights come from GED Testing Service’s official test guide. It doesn’t publish a question count per topic, so any count here is our estimate.
The 4 mistakes that cost the most points
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 adds the exponents (3⁴ × 3² = 3⁶), dividing subtracts them (3⁴ ÷ 3² = 3²), and a power of a power multiplies them ((3⁴)² = 3⁸). Wrong choices swap these, or change the base to 9, and the base never changes. If you’re unsure, write the threes out and count them.
2Reading a negative exponent as a negative number
Count down the powers of 10: 100, 10, 1, then 1/10. Each step down divides by 10, so 10⁰ = 1 and 10⁻¹ = 1/10. In the same way, 5⁻² means 1 over 5², which is 1/25, a small positive number. It isn’t −25 or −10, and 8⁰ equals 1.
3Halving instead of taking a square root
A square garden covers 144 square feet. Tempting answers for a side are 72 (half) and 36 (a quarter). Picture it as floor tiles: 144 tiles make 12 rows of 12, so the side is √144 = 12. Check every root by multiplying it back out.
4Moving the decimal point the wrong way
Think of an elevator: big numbers go up with a positive exponent, and numbers smaller than 1 go down with a negative one. 0.00052 becomes 5.2 × 10⁻⁴, four places to the right. The choices will include 5.2 × 10⁴ and 5.2 × 10⁻³. The number in front must be at least 1 and less than 10, so 52 × 10⁻⁵ is the wrong form even though it has the right value.
One problem, worked out step by step
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?
The working
- 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) - Divide the front numbers
This part is ordinary decimal arithmetic: half of 8.4 is 4.2.
8.4 ÷ 2 = 4.2 - 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 - 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 get better at this, fast
- When a rule won’t come back to you, write the powers out. 2⁵ × 2² is five twos times two more twos, seven twos in all, so the answer is 2⁷.
- Learn the squares up to 15² = 225 and the cubes up to 6³ = 216. Put them on a card and run through it on the bus. They turn √169 or ∛125 into an instant answer when there’s no calculator.
- For scientific notation, decide the sign first. A number bigger than 10 gets a positive exponent and a number smaller than 1 gets a negative one. Then check that the front number is between 1 and 10.
- Learn the calculator keys before test day. The official calculator reference sheet shows the power, root and scientific-notation keys, and knowing them saves you a minute of hunting.
Frequently asked questions
Are the exponent rules on the GED formula sheet?
No. The sheet has no exponent or root rules, so the three rules have to come from memory, along with what zero and negative exponents mean.
Can I use the calculator for square roots and cube roots?
Yes, for most of the test. The first five or so questions have no calculator, so knowing the small perfect squares and cubes by heart helps.
Is scientific notation on the GED math test?
Yes. Expect to convert in both directions, compare values written in different forms, and now and then divide two numbers in scientific notation.
How many exponent questions are on the GED?
There’s no official count per topic. Our estimate is two to four questions, based on the 25% weight this topic shares with three others.
Keep going
The GED calculator, explained
Where the power, root and scientific-notation keys are, and when you may use them.
Expressions and polynomials practice
The product rule is what makes x³ · x² = x⁵ work, so this is the next step.
Geometry and measurement practice
Square roots come from areas and cube roots from volumes.