Question

Write each expression in the form Ax^(m)y^(n) where A is a real number and m and n are integers. ((6x^(5)y)/(x^(4)y))-:((y)/(2)*(yx^(2))/(xy))

Answer 1

Explanation:

Let's simplify the given expression step by step:

((6x^(5)y)/(x^(4)y))-:((y)/(2)*(yx^(2))/(xy))

First, let's simplify the numerator of the first fraction:

6x^(5)y divided by x^(4)y equals 6x^(5-4)y^(1-1) = 6x^(1)y^(0) = 6x.

Now, let's simplify the numerator of the second fraction:

yx^(2) divided by xy equals yx^(2-1)y^(1-1) = yx^(1)y^(0) = yx.

Combining the simplified numerators, we have:

((6x)/(1)) -: ((y)/(2)) * (yx)

Now, let's simplify the denominator of the second fraction:

(y)/(2) multiplied by yx equals (y/2)yx^(1+1)y^(0+1) = (y/2)yx^(2)y^(1) = (y/2)x^(2)y^(2).

Combining the simplified denominator, we have:

((6x)/(1)) -: ((y/2)x^(2)y^(2))

Now, let's simplify the expression further:

(6x) -: ((y/2)x^(2)y^(2)) = 6x / ((y/2)x^(2)y^(2))

To rewrite this expression in the form Ax^(m)y^(n), we need to combine all the factors together. Let's rewrite it:

(6 / (y/2)) * (x^(1-2)) * (y^(0-2))

Simplifying further, we have:

(6 * 2 / y) * (x^(-1)) * (y^(-2))

12/y * (1/x) * (1/y^(2))

12/(xy^(3))

Therefore, the expression ((6x^(5)y)/(x^(4)y))-:((y)/(2)*(yx^(2))/(xy)) can be written in the form 12/(xy^(3)).