Chapter 7.4, Problem 1STP

For Exercises $1-6,$ choose the correct letter.

Which of the following is equivalent to $\frac{x^5{y}^2}{x{y}^2}$

when $x\ne 0$ and $y\ne 0?$

A. $x^6{y}^{\frac{5}{2}}$

B. $x^{5}y$

C. $x^{4}y$

D. $x^4{y}^{\frac{3}{2}}$

To determine

To determine the correct option.

Answer to Problem 1STP

Option D is correct.

Explanation of Solution

Given information:

Given expression is,

  $\frac{x^5{y}^2}{x{y}^{\frac{1}{2}}},x\ne 0,y\ne 0$

Here we shall simplify the given expression.

Here we shall use following identities,

  $\begin{array}{l}\frac{1}{x^a}=x^{-a}\\ x^a\cdot x^b=x^{a+b}\end{array}$

Now we get,

  $\begin{array}{c}\frac{x^5{y}^2}{x{y}^{\frac{1}{2}}}=\left(x^5{y}^2\right)\left(x^{-1}{y}^{-\frac{1}{2}}\right)\\ =x^{5+\left(-1\right)}{y}^{2+\left(-\frac{1}{2}\right)}\\ =x^4{y}^{\frac{3}{2}}\end{array}$

Hence option D is correct.