Certainly! Let's simplify the expression [tex]\(\left(x^2\right)^3\)[/tex].
### Step-by-Step Solution
1. Understanding the Expression:
The given expression is [tex]\(\left(x^2\right)^3\)[/tex], which means we have to raise [tex]\(x^2\)[/tex] to the power of 3.
2. Applying the Power of a Power Rule:
There is a mathematical rule known as the "power of a power" rule, which states that:
[tex]\[
\left(a^m\right)^n = a^{m \cdot n}
\][/tex]
This rule applies to exponents and can simplify expressions where an exponent is raised to another exponent.
3. Identifying the Components:
- Here, [tex]\(a\)[/tex] is [tex]\(x\)[/tex].
- [tex]\(m\)[/tex] is 2 (from [tex]\(x^2\)[/tex]).
- [tex]\(n\)[/tex] is 3 (from the outer exponent).
4. Applying the Rule:
Using the power of a power rule, we substitute [tex]\(a = x\)[/tex], [tex]\(m = 2\)[/tex], and [tex]\(n = 3\)[/tex] into the equation:
[tex]\[
\left(x^2\right)^3 = x^{2 \cdot 3}
\][/tex]
5. Simplifying the Expression:
Multiply the exponents:
[tex]\[
x^{2 \cdot 3} = x^6
\][/tex]
### Final Answer
Thus, the simplified form of the expression [tex]\(\left(x^2\right)^3\)[/tex] is:
[tex]\[
x^6
\][/tex]
