which expression is equivalent to $\frac{10x^{6}y^{12}}{-5x^{-2}y^{-6}}$? assume $x\neq0,y\neq0$.\n…

which expression is equivalent to $\frac{10x^{6}y^{12}}{-5x^{-2}y^{-6}}$? assume $x\neq0,y\neq0$.\n- $-50x^{8}y^{18}$\n- $-2x^{8}y^{18}$\n- $-2x^{12}y^{72}$\n- $5x^{8}y^{18}$

which expression is equivalent to $\frac{10x^{6}y^{12}}{-5x^{-2}y^{-6}}$? assume $x\neq0,y\neq0$.\n- $-50x^{8}y^{18}$\n- $-2x^{8}y^{18}$\n- $-2x^{12}y^{72}$\n- $5x^{8}y^{18}$

Answer

Explanation:

Step1: Divide the coefficients

Divide 10 by - 5. $\frac{10}{-5}=-2$.

Step2: Use the quotient - rule for exponents with the same base

For $x$ terms, use the rule $\frac{x^m}{x^n}=x^{m - n}$. Here $m = 6$ and $n=-2$, so $\frac{x^{6}}{x^{-2}}=x^{6-(-2)}=x^{6 + 2}=x^{8}$.

Step3: Use the quotient - rule for exponents with the same base

For $y$ terms, use the rule $\frac{y^m}{y^n}=y^{m - n}$. Here $m = 12$ and $n=-6$, so $\frac{y^{12}}{y^{-6}}=y^{12-(-6)}=y^{12 + 6}=y^{18}$.

Step4: Combine the results

The equivalent expression is $-2x^{8}y^{18}$.

Answer:

-2x^{8}y^{18} (corresponding to the second option)