Let's simplify the expression [tex]\(\left( a ^2\right)^3\)[/tex].
To simplify an expression of the form [tex]\((x^m)^n\)[/tex], you use the power of a power rule in exponents. The rule states that [tex]\((x^m)^n = x^{m \cdot n}\)[/tex], where you multiply the exponents.
Applying this rule to our given expression:
[tex]\[
\left( a^2 \right)^3
\][/tex]
We multiply the exponents:
[tex]\[
a^{2 \cdot 3} = a^6
\][/tex]
Therefore, the correct simplification of the expression [tex]\(\left( a ^2\right)^3\)[/tex] is:
[tex]\[
a^6
\][/tex]
So, the correct answer is [tex]\(a^6\)[/tex].
