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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.

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