Chapter 7.2, Problem 28PPE

To determine

To Simplify: The expression $\left(8b^{\frac{2}{3}}\cdot 9t^{\frac{1}{5}}\right)\left(8b^{\frac{5}{3}}\cdot 9t^{\frac{3}{5}}\right)$ .

Answer to Problem 28PPE

The required answer is $5184b^{\frac{7}{3}}{c}^{\frac{4}{5}}$ .

Explanation of Solution

Given information:

The expression $\left(8b^{\frac{2}{3}}\cdot 9t^{\frac{1}{5}}\right)\left(8b^{\frac{5}{3}}\cdot 9t^{\frac{3}{5}}\right)$

Calculation:

  $\begin{array}{l}\left(8b^{\frac{2}{3}}\cdot 9t^{\frac{1}{5}}\right)\left(8b^{\frac{5}{3}}\cdot 9t^{\frac{3}{5}}\right)\\ =\left(8\cdot 9\cdot 8\cdot 9\right)\left(b^{\frac{2}{3}}\cdot b^{\frac{5}{3}}\right)\left(t^{\frac{1}{5}}\cdot t^{\frac{3}{5}}\right)\end{array}$

(Commutative and associative properties of multiplication)

  $=5184\left(b^{\frac{2}{3}}\cdot b^{\frac{5}{3}}\right)\left(t^{\frac{1}{5}}\cdot t^{\frac{3}{5}}\right)$

(Simplify)

  $=5184\left(b^{\frac{2}{3}+\frac{5}{3}}\right)\left(t^{\frac{1}{5}+\frac{3}{5}}\right)$

(Add the exponents that have the same base)

  $=5184b^{\frac{7}{3}}{c}^{\frac{4}{5}}$

(Simplify the exponents)