Question

Please help answer the question.

Answer 1

a.
`(y^8)/(x^(10))`

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((x^(-4)y)/(x^(-9)y^5)\right)^(-2)\\\\=(x^((-4*-2))y^((1*-2)))/(x^((-9*-2))y^((5*-2)))\\\\=(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.

`=(x^8y^(-2))/(x^(18)y^(-10))\\\\=(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.

`=(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.

`(y^8)/(x^(10))`