Chapter 7.2, Problem 29PPE

To determine

To Simplify: The expression $\left(7d^{\frac{3}{2}}\cdot 2g^{\frac{5}{6}}\right)\left(2g^{\frac{3}{2}}\cdot 7d^{\frac{5}{6}}\right)$ .

Answer to Problem 29PPE

The required answer is $196d^{\frac{7}{3}}{g}^{\frac{7}{3}}$ .

Explanation of Solution

Given information:

The expression $\left(7d^{\frac{3}{2}}\cdot 2g^{\frac{5}{6}}\right)\left(2g^{\frac{3}{2}}\cdot 7d^{\frac{5}{6}}\right)$

Calculation:

  $\begin{array}{l}\left(7d^{\frac{3}{2}}\cdot 2g^{\frac{5}{6}}\right)\left(2g^{\frac{3}{2}}\cdot 7d^{\frac{5}{6}}\right)\\ =\left(7\cdot 2\cdot 2\cdot 7\right)\left(d^{\frac{3}{2}}\cdot d^{\frac{5}{6}}\right)\left(g^{\frac{5}{6}}\cdot g^{\frac{3}{2}}\right)\end{array}$

(Commutative and associative properties of multiplication)

  $=196\left(d^{\frac{3}{2}}\cdot d^{\frac{5}{6}}\right)\left(g^{\frac{5}{6}}\cdot g^{\frac{3}{2}}\right)$

(Simplify)

  $=196\left(d^{\frac{3}{2}+\frac{5}{6}}\right)\left(g^{\frac{5}{6}+\frac{3}{2}}\right)$

(Add the exponents that have the same base)

  $=196d^{\frac{7}{3}}{g}^{\frac{7}{3}}$

(Simplify the exponent)