which expression is equivalent to $\frac{-9x^{-1}y^{-9}}{-15x^{5}y^{-3}}$? assume $x\neq0,y\neq0$.\n$\frac{3}…

which expression is equivalent to $\frac{-9x^{-1}y^{-9}}{-15x^{5}y^{-3}}$? assume $x\neq0,y\neq0$.\n$\frac{3}{5x^{5}y^{3}}$\n$\frac{3}{5x^{6}y^{6}}$\n$\frac{5}{3x^{5}y^{3}}$\n$\frac{5}{3x^{6}y^{6}}$

which expression is equivalent to $\frac{-9x^{-1}y^{-9}}{-15x^{5}y^{-3}}$? assume $x\neq0,y\neq0$.\n$\frac{3}{5x^{5}y^{3}}$\n$\frac{3}{5x^{6}y^{6}}$\n$\frac{5}{3x^{5}y^{3}}$\n$\frac{5}{3x^{6}y^{6}}$

Answer

Answer:

B. $\frac{3}{5x^{6}y^{6}}$

Explanation:

Step1: Simplify the coefficient

Divide -9 by -15: $\frac{-9}{-15}=\frac{3}{5}$

Step2: Use exponent - subtraction rule for x

For $x$ terms, $x^{-1}\div x^{5}=x^{-1 - 5}=x^{-6}=\frac{1}{x^{6}}$

Step3: Use exponent - subtraction rule for y

For $y$ terms, $y^{-9}\div y^{-3}=y^{-9-(-3)}=y^{-6}=\frac{1}{y^{6}}$

Step4: Combine the results

The expression becomes $\frac{3}{5}\times\frac{1}{x^{6}}\times\frac{1}{y^{6}}=\frac{3}{5x^{6}y^{6}}$