Multiply and simplify. $\frac { 27 s ^ { 8 } } { 25 s } \cdot \frac { 15 s ^ { 7 } } { 243 s }$
A) $\frac { s ^ { 13 } } { 15 } , s \neq 0$
B) $\frac { s ^ { 14 } } { 3 } , s \neq 0$
C) $\frac { s ^ { 17 } } { 30 } , s \neq 0$
D) $\frac { s ^ { 16 } } { 10 } , s \neq 0$
E) $\frac { s ^ { 13 } } { 5 } , s \neq 0$

Question

Quizplus · Accepted Answer

When multiplying fractions, you multiply the numerators together and the denominators together. Simplifying the expression $\frac { 27 s ^ { 8 } } { 25 s } \cdot \frac { 15 s ^ { 7 } } { 243 s }$, 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 $s \neq 0$ 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 $s \neq 0$.

Multiply and Simplify 27s825s⋅15s7243s\frac { 27 s ^ { 8 } } { 25 s } \cdot \frac { 15 s ^ { 7 } } { 243 s }25s27s8​⋅243s15s7​

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