Chapter 5.4, Problem 26E

To determine

To simplify : The product of $-\frac{d^5}{13}\cdot \left(-\frac{3d^7}{4}\right)$ .

Answer to Problem 26E

The simplified expression is $\frac{3d^{12}}{52}$ .

Explanation of Solution

Given information :

Consider, the expression provided in the question,

  $-\frac{d^5}{13}\cdot \left(-\frac{3d^7}{4}\right)$

Solution :

The product of two fractions is equal to the product of numerator over the product of the denominator. Therefore,

  $\begin{array}{l}-\frac{d^5}{13}\cdot \left(-\frac{3d^7}{4}\right)=\frac{-d^5\cdot \left(-3d^7\right)}{13\cdot 4}\text{ (Use rule for multiplying fractions) }\\ -\frac{d^5}{13}\cdot \left(-\frac{3d^7}{4}\right)=\frac{3d^{5+7}}{52}\text{ (Multiply and use product of powers property)}\\ -\frac{d^5}{13}\cdot \left(-\frac{3d^7}{4}\right)=\frac{3d^{12}}{52}\text{ (Add the powers)}\end{array}$

Hence,

The simplified expression is $\frac{3d^{12}}{52}$ .