Chapter 4, Problem 23CR

To determine

To write the fraction in simplest form $\frac{8xy}{2x^{2}y}$

Answer to Problem 23CR

  $\frac{4}{x}$

Explanation of Solution

Given information:

Expression $\frac{8xy}{2x^{2}y}$

Formula Used: Quotient rule with same base,Zero Exponent Rule and Negative Exponent Rule

Calculation:

The Quotient Rule with same base says that when the bases are same and in division, the exponent powers are subtracted. In the given expression, have x and y in both numerator & denominator. On applying the Quotient rule,have

  $=\frac{8}{2}\times \left(\frac{x^1}{x^2}\right)\times \left(\frac{y^1}{y^1}\right)$

8 & 2 will divide to give us 4.

On applying the Quotient rule, get-

  $=4\times \left(x^{1-2}\right)\times \left(y^{1-1}\right)$

Hence,

  $=4\times \left(x^{-1}\right)\times \left(y^0\right)$

now apply the negative exponent rule to make the exponent positive and the zero exponent rule to y.

  $=\frac{4}{x}$

Conclusion-

  $=\frac{4}{x}$