Question

Use the rules of exponents to simplify the expression.
left parenthesis negative r Superscript 4 Baseline s right parenthesis Superscript 4 Baseline left parenthesis negative r cubed s cubed right parenthesis squared

Answer 1

To simplify the expression \(( -r^4 s )^4 ( -r^3 s^3 )^2\), we will apply the rules of exponents step by step.

1. **Simplify each part separately:**

- For \(( -r^4 s )^4\):
\[
( -r^4 s )^4 = (-1)^4 (r^4)^4 (s)^4 = 1 \cdot r^{16} \cdot s^4 = r^{16} s^4
\]

- For \(( -r^3 s^3 )^2\):
\[
( -r^3 s^3 )^2 = (-1)^2 (r^3)^2 (s^3)^2 = 1 \cdot r^6 \cdot s^6 = r^6 s^6
\]

2. **Combine the results:**
Now we combine the simplified parts:
\[
( -r^4 s )^4 ( -r^3 s^3 )^2 = (r^{16} s^4)(r^6 s^6)
\]

3. **Use the properties of exponents to combine:**
- For the \(r\) terms:
\[
r^{16} \cdot r^6 = r^{16 + 6} = r^{22}
\]

- For the \(s\) terms:
\[
s^4 \cdot s^6 = s^{4 + 6} = s^{10}
\]

4. **Final result:**
Putting it all together, we have:
\[
r^{22} s^{10}
\]

Thus, the simplified expression is:
\[
\boxed{r^{22} s^{10}}
\]