Chapter 9.9, Problem 8MRE

To determine

To simplify the expression $\frac{10x{y}^{-2}}{6x^{-1}{y}^3}$

Answer to Problem 8MRE

The answer is $\frac{5x^2}{3y^5}$

Explanation of Solution

Given: Expression: $\frac{10x{y}^{-2}}{6x^{-1}{y}^3}$

Formula Used:

Cancelling out the common multiple in both numerator and denominator to simplify the expression.

The rule of division for exponents with the same base.

Calculation:

Given: Expression: $\frac{10x{y}^{-2}}{6x^{-1}{y}^3}$

By striking out the common multiple in both the numerator and denominator, we get the expression,

  $\frac{5x{y}^{-2}}{3x^{-1}{y}^3}$

Further, we use the rule of division for exponents with the same base; when we divide the powers, we subtract their exponents. Hence, the above expression can be further simplified into:

  $\frac{5x^{\left\{1-\left(-1\right)\right\}}{y}^{(-2-3)}}{3}$

Further simplified version,

  $\frac{5x^2{y}^{-5}}{3}$

Thus, the above expression can be written as $\frac{5x^2}{3y^5}$

Conclusion:

Hence, the solution is $\frac{5x^2}{3y^5}$