Question

Multiply. State the product in simplest form.

4/9k^5 x 3k^3/8, k=0

Answer 1

To multiply the two expressions \( \frac{4}{9}k^5 \) and \( \frac{3k^3}{8} \), we follow these steps:

1. **Multiply the numerators**:
\[
4 \times 3k^5 \times k^3 = 12k^{5+3} = 12k^8
\]

2. **Multiply the denominators**:
\[
9 \times 8 = 72
\]

3. **Combine them**:
\[
\frac{12k^8}{72}
\]

4. **Simplify the fraction**:
We can simplify \( \frac{12}{72} \) which becomes \( \frac{1}{6} \):
\[
\frac{12k^8}{72} = \frac{12}{72}k^8 = \frac{1}{6}k^8
\]

Now, because you stated \( k = 0 \), substituting \( k = 0 \) into the expression gives:
\[
\frac{1}{6} \times 0^8 = \frac{1}{6} \times 0 = 0
\]

Thus, the product in simplest form is:
\[
\text{Product} = 0
\]