The expression which is equivalent to the expression for x^(-3) from the given by: Option C: 1/x³
What are equivalent expressions?
Those expressions who might look different but their simplified forms are same expressions are called equivalent expressions.
To derive equivalent expressions of some expression, we can either make it look more complex or simple. Usually, we simplify it.
What are some basic properties of exponentiation?
If we have a^b then 'a' is called base and 'b' is called power or exponent and we call it "a is raised to the power b" (this statement might change from text to text slightly).
Exponentiation(the process of raising some number to some power) have some basic rules as:
[tex]a^{-b} = \dfrac{1}{a^b}\\\\a^0 = 1 (a \neq 0)\\\\a^1 = a\\\\(a^b)^c = a^{b \times c}\\\\ a^b \times a^c = a^{b+c} \\\\^n\sqrt{a} = a^{1/n} \\\\(ab)^c = a^c \times b^c\\\\a^b = a^b \implies b= c \: \text{ (if a, b and c are real numbers and } a \neq 1 \: and \: a \neq -1 )[/tex]
The given expression is: [tex]x^{-3}[/tex]
From the first property listed, we get:
[tex]x^{-3} = \dfrac{1}{x^3}[/tex]
(we can derive it too as [tex]x^{-3} = x^{0-3} = \dfrac{x^0}{x^3} = \dfrac{1}{x^3}[/tex] )
Thus, the expression which is equivalent to the expression for x^(-3) from the given by: Option C; 1/x³
Learn more about exponentiation here:
https://brainly.com/question/26938318
