which expression is equivalent to $\frac{3x^{-6}y^{-3}}{15x^{2}y^{10}}$? assume $x\neq0,y\neq0$.\n$\frac{5}{x…

which expression is equivalent to $\frac{3x^{-6}y^{-3}}{15x^{2}y^{10}}$? assume $x\neq0,y\neq0$.\n$\frac{5}{x^{12}y^{30}}$\n$\frac{1}{5x^{8}y^{13}}$\n$\frac{5}{x^{4}y^{7}}$\n$\frac{y^{7}}{5x^{4}}$

which expression is equivalent to $\frac{3x^{-6}y^{-3}}{15x^{2}y^{10}}$? assume $x\neq0,y\neq0$.\n$\frac{5}{x^{12}y^{30}}$\n$\frac{1}{5x^{8}y^{13}}$\n$\frac{5}{x^{4}y^{7}}$\n$\frac{y^{7}}{5x^{4}}$

Answer

Explanation:

Step1: Simplify the coefficient

Divide 3 by 15: $\frac{3}{15}=\frac{1}{5}$

Step2: Use the quotient - rule for exponents ($\frac{a^m}{a^n}=a^{m - n}$) for $x$ terms

For $x$ terms, we have $\frac{x^{-6}}{x^{2}}=x^{-6-2}=x^{-8}=\frac{1}{x^{8}}$

Step3: Use the quotient - rule for exponents for $y$ terms

For $y$ terms, $\frac{y^{-3}}{y^{10}}=y^{-3 - 10}=y^{-13}=\frac{1}{y^{13}}$

Step4: Combine the results

The simplified expression is $\frac{1}{5}\times\frac{1}{x^{8}}\times\frac{1}{y^{13}}=\frac{1}{5x^{8}y^{13}}$

Answer:

$\frac{1}{5x^{8}y^{13}}$ (corresponding to the second option in the multiple - choice list)