Answer:
a. [tex]\dfrac{y^8}{x^{10}}[/tex]
Step-by-step explanation:
First step is ti distribute the exponent outside the parenthesis. According to the law of exponents, you need to distribute it to each variable.
[tex]\left(\dfrac{x^{-4}y}{x^{-9}y^5}\right)^{-2}\\\\=\dfrac{x^{(-4\times-2)}y^{(1\times-2)}}{x^{(-9\times-2)}y^{(5\times-2)}}\\\\=\dfrac{x^{8}y^{-2}}{x^{18}y^{-10}}[/tex]
Now again, following the law of exponents, if you have negative exponents, you put them in the opposite side of the fraction.
[tex]=\dfrac{x^8y^{-2}}{x^{18}y^{-10}}\\\\=\dfrac{x^8y^{10}}{x^{18}y^{2}}\\\\[/tex]
Next, when it comes to division, we subtract the exponents of the numerator and the denominator of similar variables.
[tex]=\dfrac{x^8y^{10}}{x^{18}y^{2}}\\\\=x^{(8-18)}y^{(10-2)}\\\\=x^{-10}y^8[/tex]
Since the exponent of x is negative, we move it below the fraction.
[tex]\dfrac{y^8}{x^{10}}[/tex]
