Radicals and Rational Exponents
Aligned to N-RN.A.2 — Common Core State Standards for Mathematics.
What this lesson teaches
Any radical can be written as a rational exponent: the nth root of a^m equals a^(m/n). Switching to exponent form lets you simplify using the ordinary rules for exponents.
Worked example
Simplify 16^(3/4). Write it as (16^(1/4))^3. Since 16^(1/4) = 2 (because 2^4 = 16), this becomes 2^3 = 8. So 16^(3/4) = 8.
Practice questions
- Rewrite √(x^3) using a rational exponent.
- Evaluate 32^(2/5).
- Simplify (x^(1/2) × x^(1/3)) as a single power of x.
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Every lesson comes with a video taught in English and Spanish — the same video the QR code in the printed workbook opens.
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Radicales y Exponentes Racionales
Todo radical se puede escribir como exponente racional: la raíz enésima de a^m es igual a a^(m/n). Cambiar a la forma de exponente permite simplificar usando las reglas comunes de exponentes.
Ejemplo: Simplifica 16^(3/4). Escríbelo como (16^(1/4))^3. Como 16^(1/4) = 2 (porque 2^4 = 16), queda 2^3 = 8. Así que 16^(3/4) = 8.
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