Multiply and simplify. $\frac{27s^8}{25s}\cdot \frac{15s^7}{243s}$

A) $\frac{s^{13}}{15},s\ne 0$
B) $\frac{s^{14}}{3},s\ne 0$
C) $\frac{s^{17}}{30},s\ne 0$
D) $\frac{s^{16}}{10},s\ne 0$
E) $\frac{s^{13}}{5},s\ne 0$

When multiplying fractions, you multiply the numerators together and the denominators together. Simplifying the expression $\frac{27s^8}{25s}\cdot \frac{15s^7}{243s}$ , you get $\frac{27\cdot 15\cdot s^8\cdot s^7}{25\cdot 243\cdot s\cdot s}$ . Simplifying further, $27\cdot 15=405$ and $25\cdot 243=6075$ , which simplifies to $\frac{1\cdot s^{15}}{15}$ , or $\frac{s^{15}}{15}$ , considering $s\ne 0$ to avoid division by zero. However, it seems there was a mistake in my calculation of the powers of $s$ and the simplification of the coefficients. Correctly simplifying the powers of $s$ gives $s^{8+7-1-1}=s^{13}$ , and correctly simplifying the coefficients gives $\frac{405}{6075}=\frac{1}{15}$ , leading to the correct answer of $\frac{s^{13}}{15}$ , with the condition $s\ne 0$ .