Simplify the following expression using the properties of exponents. The final form of the expressions with variables should contain only positive exponents. Assume that all variables represent nonzero numbers.
\[
\frac{20 x^{9} \cdot 2 x^{-6}}{8 y x^{3}}
\]
Answer
Final Answer: \(\boxed{\frac{5}{y}}\)
Step 1 ：Given the expression \(\frac{20 x^{9} \cdot 2 x^{-6}}{8 y x^{3}}\)
Step 2 ：First, simplify the numerator by combining like terms. This gives us \(40 x^{9-6} = 40 x^{3}\)
Step 3 ：Then, simplify the denominator by combining like terms. This gives us \(8 y x^{3}\)
Step 4 ：Next, divide the numerator by the denominator. This gives us \(\frac{40 x^{3}}{8 y x^{3}}\)
Step 5 ：Simplify the expression by cancelling out \(x^{3}\) from the numerator and the denominator and dividing 40 by 8. This gives us \(\frac{5}{y}\)
Step 6 ：Final Answer: \(\boxed{\frac{5}{y}}\)
