Chapter 9.9, Problem 9MRE

To determine

To simplify the expression $\frac{18x^{3}y}{30x^2{y}^4}$

Answer to Problem 9MRE

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

Explanation of Solution

Given: Expression: $\frac{18x^{3}y}{30x^2{y}^4}$

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: $\frac{18x^{3}y}{30x^2{y}^4}$

The above expression can be written as:

  $\frac{(3\times 6)x^{3}y}{(5\times 6)x^2{y}^4}$

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

  $\frac{3x^{3}y}{5x^2{y}^4}$

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:

  $\frac{3x^{\left(3-2\right)}{y}^{(1-4)}}{5}$

Further simplified version,

  $\frac{3x{y}^{-3}}{5}$

Thus, the above expression can be written as -

  $\frac{3x}{5y^3}$

Conclusion:

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