Sure, let's address each expression one by one and simplify them:
### a) [tex]\( x^{12} \)[/tex]
This expression is already in its simplest form. Thus, the reduced form of [tex]\( x^{12} \)[/tex] is:
[tex]\[ x^{12} \][/tex]
### b) [tex]\( x \)[/tex]
This expression is already in its simplest form, as [tex]\( x \)[/tex] represents the variable itself. Thus, the reduced form of [tex]\( x \)[/tex] is:
[tex]\[ x \][/tex]
### c) [tex]\( x^{10} \)[/tex]
This expression is already in its simplest form. Thus, the reduced form of [tex]\( x^{10} \)[/tex] is:
[tex]\[ x^{10} \][/tex]
### d) [tex]\( x^5 \)[/tex]
This expression is already in its simplest form. Thus, the reduced form of [tex]\( x^5 \)[/tex] is:
[tex]\[ x^5 \][/tex]
### e) [tex]\( x^{-2} \)[/tex]
For this expression, we note that a negative exponent signifies the reciprocal of the variable raised to the positive exponent. Therefore:
[tex]\[ x^{-2} = \frac{1}{x^2} \][/tex]
Although we have simplified our expressions as much as possible, it is crucial to remember that each one was already in its most simplified form or had a straightforward transformation.
To summarize, the reduced forms are:
a) [tex]\( x^{12} \)[/tex] remains [tex]\( x^{12} \)[/tex]
b) [tex]\( x \)[/tex] remains [tex]\( x \)[/tex]
c) [tex]\( x^{10} \)[/tex] remains [tex]\( x^{10} \)[/tex]
d) [tex]\( x^5 \)[/tex] remains [tex]\( x^5 \)[/tex]
e) [tex]\( x^{-2} \)[/tex] can be written as [tex]\( \frac{1}{x^2} \)[/tex] but is also often denoted as [tex]\( x^{-2} \)[/tex] in its simplified form.
However, the expressions certainly can be listed as given initially:
1. [tex]\( x^{12} \)[/tex]
2. [tex]\( x^5 \)[/tex]
3. [tex]\( x \)[/tex]
4. [tex]\( x^{-2} \)[/tex]
5. [tex]\( x^{10} \)[/tex]
