Question

divide. state any restrictions on the variables
\\(\frac{3x^5}{7y^4} \div \frac{6y^{-5}}{7x^{-7}}\\)

simplify the rational expression.
\\(\frac{3x^5}{7y^4} \div \frac{6y^{-5}}{7x^{-7}} = \square\\)
(simplify your answer. use integers or fractions for any numbers in the expression.)
what are the restrictions on the variables? select the correct choice below and, if necessary, fill in the answer box to complete your choice.
\\(\bigcirc\\) a. \\(x \
eq \square\\) and \\(y \
eq \square\\)
(use a comma to separate answers as needed.)
\\(\bigcirc\\) b. there are no restrictions on the variables.

Explanation:

Step1: Rewrite division as multiplication

$\frac{3x^5}{7y^4} \div \frac{6y^{-5}}{7x^{-7}} = \frac{3x^5}{7y^4} \times \frac{7x^{-7}}{6y^{-5}}$

Step2: Multiply numerators and denominators

$\frac{3x^5 \times 7x^{-7}}{7y^4 \times 6y^{-5}}$

Step3: Simplify coefficients and exponents

$\frac{3 \times 7}{7 \times 6} \times x^{5+(-7)} \times y^{-4-(-5)} = \frac{1}{2}x^{-2}y^{1}$

Step4: Rewrite positive exponents only

$\frac{y}{2x^2}$

Step5: Identify variable restrictions

Denominators cannot be 0, so $x
eq 0$ and $y
eq 0$.

Answer:

Simplified expression: $\boldsymbol{\frac{y}{2x^2}}$
Restrictions: A. $x
eq 0$ and $y
eq 0$