Question

divide and simplify.
\\(\dfrac{49x^3}{7x^4} \div \dfrac{7x^5}{5x^6}\\)

the simplified quotient is \\(\square\\).

Explanation:

Step1: Rewrite division as multiplication

To divide two fractions, we multiply the first fraction by the reciprocal of the second fraction. So, \(\frac{49x^{3}}{7x^{4}} \div \frac{7x^{5}}{5x^{6}}=\frac{49x^{3}}{7x^{4}}\times\frac{5x^{6}}{7x^{5}}\)

Step2: Simplify coefficients and variables separately

For the coefficients: \(\frac{49\times5}{7\times7}\). \(49\div7 = 7\), then \(7\times5\div7=5\).
For the variables with \(x\): Use the rule \(x^{a}\times x^{b}=x^{a + b}\) and \(\frac{x^{a}}{x^{b}}=x^{a - b}\). So for \(x\) terms: \(\frac{x^{3}\times x^{6}}{x^{4}\times x^{5}}=\frac{x^{3 + 6}}{x^{4+5}}=\frac{x^{9}}{x^{9}} = 1\) (since \(x^{a}\div x^{a}=1\) for \(x
eq0\)).

Step3: Multiply the results

Multiply the coefficient result and the variable result: \(5\times1 = 5\).

Answer:

\(5\)