Find the best solutions to your questions at Westonci.ca, the premier Q&A platform with a community of knowledgeable experts. Get detailed and precise answers to your questions from a dedicated community of experts on our Q&A platform. Explore comprehensive solutions to your questions from a wide range of professionals on our user-friendly platform.

X to the power of -3 = 1/x to the 3rd power what property is this

Sagot :

Answer:

Step-by-step explanation:

The expression \( x^{-3} = \frac{1}{x^3} \) illustrates the property of **negative exponents**. Specifically, this property states:

\[ x^{-n} = \frac{1}{x^n} \]

where \( n \) is a positive integer. This property tells us that a negative exponent on a variable or number is equivalent to taking the reciprocal and applying a positive exponent of the same magnitude. Therefore, \( x^{-3} \) is equal to \( \frac{1}{x^3} \) because raising \( x \) to the power of -3 is the same as taking the reciprocal of \( x^3 \).

This property is fundamental in simplifying expressions involving negative exponents and understanding how exponents behave in algebraic equations and identities.