Exponents and Scientific Notation
Aligned to 8.EE.A.1 — Common Core State Standards for Mathematics.
What this lesson teaches
The laws of exponents let you combine powers quickly: when you multiply powers with the same base you add the exponents. Scientific notation writes a number as a value between 1 and 10 times a power of ten, which makes very large or very small numbers easy to handle.
Worked examples
Example 1
Simplify 10 squared times 10 cubed by adding exponents: 2 + 3 is 5, so the answer is 10 to the 5th. Write 4,000 in scientific notation as 4 times 10 to the 3rd.
Example 2
Simplify 5⁷ ÷ 5⁴ by subtracting exponents: 7 − 4 = 3, so the answer is 5³ = 125.
Example 3
A negative exponent means a reciprocal: 2⁻³ = 1/2³ = 1/8. It does not make the number negative.
Practice questions
- Simplify x to the 2nd times x to the 4th.
- Write 52,000 in scientific notation.
- What is 10 to the 0 power?
Watch the lesson
Every lesson comes with a video taught in English and Spanish — the same video the QR code in the printed workbook opens.
▶ Watch this lessonEn español
Exponentes y Notación Científica
Las leyes de los exponentes te permiten combinar potencias rápidamente: cuando multiplicas potencias con la misma base, sumas los exponentes. La notación científica escribe un número como un valor entre 1 y 10 multiplicado por una potencia de diez, lo que facilita el manejo de números muy grandes o muy pequeños.
Ejemplo 1: Simplifica 10 al cuadrado por 10 al cubo sumando los exponentes: 2 + 3 es 5, así que la respuesta es 10 a la 5ta potencia. Escribe 4,000 en notación científica como 4 por 10 a la 3ra potencia.
Ejemplo 2: Simplifica 5⁷ ÷ 5⁴ restando los exponentes: 7 − 4 = 3, así que la respuesta es 5³ = 125.
Ejemplo 3: Un exponente negativo significa recíproco: 2⁻³ = 1/2³ = 1/8. No hace negativo al número.
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