Chapter 7.2, Problem 2LC

To determine

To Write: The simplified form of $2n^{\frac{2}{3}}\cdot 3n^{\frac{3}{4}}$ .

Answer to Problem 2LC

The required answer is $6n^{\frac{17}{12}}$ .

Explanation of Solution

Given information:

The expression $2n^{\frac{2}{3}}\cdot 3n^{\frac{3}{4}}$

Calculation:

  $\begin{array}{l}2n^{\frac{2}{3}}\cdot 3n^{\frac{3}{4}}\\ =\left(2\cdot 3\right)\left(n^{\frac{2}{3}}\cdot n^{\frac{3}{4}}\right)\end{array}$

(Commutative and associative properties of multiplication)

  $=6\left(n^{\frac{2}{3}}\cdot n^{\frac{3}{4}}\right)$

(Simplify)

  $=6\left(n^{\frac{2}{3}+\frac{3}{4}}\right)$

(Add the exponents that have the same base)

  $=6n^{\frac{17}{12}}$

(Simplify the exponents)