Rational Exponents
Aligned to N-RN.A.1 — Common Core State Standards for Mathematics.
What this lesson teaches
To keep the rule (a^m)^n = a^(m×n) working for fractions, we define a^(1/n) as the number whose nth power is a. So a^(1/n) is the nth root of a, and a^(m/n) means (nth root of a)^m.
Worked example
Evaluate 8^(2/3). First 8^(1/3) = 2, because 2^3 = 8. Then 8^(2/3) = (8^(1/3))^2 = 2^2 = 4.
Practice questions
- Write 5^(1/2) as a radical.
- Evaluate 27^(1/3).
- Evaluate 16^(3/4).
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 Racionales
Para que la regla (a^m)^n = a^(m×n) siga funcionando con fracciones, definimos a^(1/n) como el número cuya potencia n es a. Así, a^(1/n) es la raíz n de a, y a^(m/n) significa (raíz n de a)^m.
Ejemplo: Evalúa 8^(2/3). Primero 8^(1/3) = 2, porque 2^3 = 8. Luego 8^(2/3) = (8^(1/3))^2 = 2^2 = 4.
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