5 Questions
¿Cuál es la fórmula para encontrar el producto de potencias?
(ab)^n = a^n * b^n
¿Cuál es el resultado de (2^3)^2?
2^6
¿Cuál es el valor de a^0?
1
¿Cuál es la fórmula para encontrar la nth raíz de un número?
x = nth root of a ⇔ x^n = a
¿Cuál es el resultado de x^3 = 27?
x = 3
Study Notes
Exponentiation and Root Extraction
Power of a Product
- The power of a product is the product of the powers of the individual factors.
- Formula:
(ab)^n = a^n * b^n - Example:
(2x)^3 = 2^3 * x^3 = 8x^3
Power of a Power
- The power of a power is the power raised to another power.
- Formula:
(a^n)^m = a^(n*m) - Example:
(2^3)^2 = 2^(3*2) = 2^6 = 64
Zero Exponent
- Any non-zero number raised to the power of zero is equal to 1.
- Formula:
a^0 = 1 - Exception:
0^0is undefined in standard arithmetic, but may have specific values in certain mathematical contexts.
nth Root
- The nth root of a number is a value that, when raised to the power of n, gives the original number.
- Formula:
x = nth root of a ⇔ x^n = a - Example:
x = 3rd root of 27 ⇔ x^3 = 27 - Note: The nth root of a number can be positive or negative, depending on the value of n.
Learn about the rules of exponentiation including the power of a product, power of a power, and zero exponent. Also, learn about nth roots and how to calculate them.
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