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Powers of ten, from tiny to huge

Multiply and divide powers of ten, use a zero or negative exponent, and compare numbers written in scientific notation.

By FinishHigh · Published 2026-10-27 · Updated 2026-10-27

A power is repeated multiplication

10³ means 10 × 10 × 10, which is 1,000. The small raised number, the exponent, counts how many times the base is a factor. It is not the same as 10 × 3.

When the bases match, you can combine them. To multiply, add the exponents: 10³ × 10² = 10⁵. To divide, subtract them: 10⁶ ÷ 10² = 10⁴. Check a small case. 10² × 10¹ = 100 × 10 = 1,000, and 10³ is also 1,000.

Zero and negative exponents

Any nonzero number to the power 0 equals 1. So 7⁰ = 1 and 10⁰ = 1. Zero to the power zero is not used here.

A negative exponent means a reciprocal, not a negative number. 10⁻³ = 1/10³ = 0.001. The result is small and positive. 10⁻³ is not −1,000 and it is not −30.

Scientific notation keeps the zeros in the exponent

A number in scientific notation has one digit before the decimal, then × 10 to a power. 4.2 × 10⁵ means 4.2 × 100,000 = 420,000. 9.1 × 10⁴ means 91,000. Compare the powers first: 10⁵ is ten times 10⁴, so 4.2 × 10⁵ is larger even though 4.2 is smaller than 9.1.

To multiply (3 × 10⁴) × (2 × 10³), multiply the front numbers and add the exponents: 3 × 2 = 6 and 10⁴ × 10³ = 10⁷, so the product is 6 × 10⁷. If the front number were 10 or more, you would shift the decimal and adjust the exponent. 6 is already between 1 and 10, so it stays.

What this lesson is

This is an original FinishHigh lesson for practice. It is not a GED® test form, not an official item, and not a readiness score. The public GED® Mathematical Reasoning materials describe quantitative problem solving, including exponents and scientific notation, as part of math study. Those outlines were used only as a topic list. No question text or figure was copied.

A related measurement habit: convert units before you compare. 5 feet is 5 × 12 = 60 inches. 90 minutes is 90 ÷ 60 = 1.5 hours.

Try this next: 6 questions ↓

ORIGINAL PRACTICE

Your turn.

Try each question before opening the explanation. These are FinishHigh practice examples, not GED® test questions.

Simplify 10⁴ × 10³.
Show the answer and why
10⁷. The bases match, so add the exponents: 4 + 3 = 7. That is 10,000,000, not 10¹² and not 10 × 7.
Simplify 10⁸ ÷ 10⁵.
Show the answer and why
10³. Subtract the exponents: 8 − 5 = 3. Check: 100,000,000 ÷ 100,000 = 1,000.
What is 9⁰? What is 10⁻²?
Show the answer and why
9⁰ = 1, because a nonzero number to the power 0 is 1. 10⁻² = 1/100 = 0.01. It is positive and small, not −100.
Multiply (4 × 10³) × (2 × 10²). Write the product in scientific notation.
Show the answer and why
8 × 10⁵. Multiply 4 × 2 = 8 and add the exponents 3 + 2 = 5. 8 is already one digit before the decimal, so the exponent stays 5.
Which is larger, 3.5 × 10⁶ or 8.2 × 10⁵? How do you know?
Show the answer and why
3.5 × 10⁶ is larger. 10⁶ is 1,000,000 and 10⁵ is 100,000, so the first number is about 3,500,000 and the second is about 820,000. Compare the powers of ten before the front numbers.
A shelf is 4 feet long. How many inches is that? A timer reads 150 minutes. How many hours is that?
Show the answer and why
4 × 12 = 48 inches. 150 ÷ 60 = 2.5 hours. Convert with the unit relationship, then do the arithmetic.