Question

Please help answer the question.

Answer 1

Answer:

a. $\dfrac{y^8}{x^{10}}$

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.

$\left(\dfrac{x^{-4}y}{x^{-9}y^5}\right)^{-2}\\\\=\dfrac{x^{(-4\times-2)}y^{(1\times-2)}}{x^{(-9\times-2)}y^{(5\times-2)}}\\\\=\dfrac{x^{8}y^{-2}}{x^{18}y^{-10}}$

Now again, following the law of exponents, if you have negative exponents, you put them in the opposite side of the fraction.

$=\dfrac{x^8y^{-2}}{x^{18}y^{-10}}\\\\=\dfrac{x^8y^{10}}{x^{18}y^{2}}$

Next, when it comes to division, we subtract the exponents of the numerator and the denominator of similar variables.

$=\dfrac{x^8y^{10}}{x^{18}y^{2}}\\\\=x^{(8-18)}y^{(10-2)}\\\\=x^{-10}y^8$

Since the exponent of x is negative, we move it below the fraction.

$\dfrac{y^8}{x^{10}}$