Sure, let's simplify the expression [tex]\( \left(r^4 s^2\right)^2 \)[/tex] step-by-step.
1. Rewrite the expression inside the parentheses:
The expression inside the parentheses is [tex]\( r^4 s^2 \)[/tex].
2. Apply the exponent to each term inside the parentheses:
When an expression [tex]\((ab)^c\)[/tex] is raised to a power, we apply the power [tex]\(c\)[/tex] to each factor inside the parentheses separately. Thus, we have:
[tex]\[
\left(r^4 s^2\right)^2 = \left(r^4\right)^2 \cdot \left(s^2\right)^2
\][/tex]
3. Simplify each term:
Now we will simplify each term separately:
- For [tex]\( \left(r^4\right)^2 \)[/tex], we use the rule of exponents [tex]\((x^a)^b = x^{a \cdot b}\)[/tex]. Applying this rule gives:
[tex]\[
\left(r^4\right)^2 = r^{4 \cdot 2} = r^8
\][/tex]
- For [tex]\( \left(s^2\right)^2 \)[/tex], we apply the same rule:
[tex]\[
\left(s^2\right)^2 = s^{2 \cdot 2} = s^4
\][/tex]
4. Combine the simplified terms:
After simplifying each term, we can combine them:
[tex]\[
\left(r^4 s^2\right)^2 = r^8 \cdot s^4
\][/tex]
So, the simplified expression is:
[tex]\[
r^8 s^4
\][/tex]
