Answer:
Option B and D are correct
[tex](x^{-3})^2[/tex] or
[tex]x^6 \cdot x^{-12}[/tex]
Step-by-step explanation:
Using exponent rule:
[tex](ab)^m = a^m \cdot b^m[/tex]
[tex](a^m)^n = a^{mn}[/tex]
[tex]a^m \cdot a^n = a^{m+n}[/tex]
Given the expression:
[tex](x^3 \cdot x^{-6})^2[/tex] ....[1]
Apply the exponent rule:
[tex](x^{3-6})^2[/tex]
[tex](x^{-3})^2[/tex]
We can write the given expression as:
Apply the exponent rule in [1]:
[tex](x^3)^2 \cdot (x^{-6})^2[/tex]
⇒[tex]x^6 \cdot x^{-12}[/tex]
Therefore, the first step in simplifying this expression are:
[tex](x^{-3})^2[/tex] or [tex]x^6 \cdot x^{-12}[/tex]
