Certainly! Let's simplify the given expression step-by-step.
We start with the expression:
[tex]\[
\left( y^4 \right)^2
\][/tex]
To simplify this, we can use the power of a power rule in exponents. The power of a power rule states that \((a^m)^n = a^{m \cdot n}\).
Here, our base \(a\) is \(y\), the exponent \(m\) is \(4\), and the outer exponent \(n\) is \(2\). According to the rule:
[tex]\[
\left( y^4 \right)^2 = y^{4 \cdot 2}
\][/tex]
Multiplying the exponents \(4 \times 2\) gives us:
[tex]\[
4 \times 2 = 8
\][/tex]
Thus, we can rewrite the expression as:
[tex]\[
y^8
\][/tex]
So, the simplified form of \(\left( y^4 \right)^2\) in the form \(y^n\) is:
[tex]\[
y^8
\][/tex]
This concludes our simplification. The answer is:
[tex]\[
y^8
\][/tex]
