Chapter 7.2, Problem 49PPE

To determine

To Simplify: The expression $3^{\frac{1}{4}}\cdot 2^y\cdot 3^2\cdot 2^x$

Answer to Problem 49PPE

The required answer is $3^{\frac{9}{4}}{2}^{y+x}$ .

Explanation of Solution

Given information:

The expression $3^{\frac{1}{4}}\cdot 2^y\cdot 3^2\cdot 2^x$

Calculation:

  $\begin{array}{l}{3}^{\frac{1}{4}}\cdot 2^y\cdot 3^2\cdot 2^x\\ =\left(3^{\frac{1}{4}}\cdot 3^2\right)\left(2^y\cdot 2^x\right)\end{array}$

(Commutative and associative properties of multiplication)

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

(Add the exponents that have the same base)

  $=3^{\frac{9}{4}}{2}^{y+x}$

(Simplify the exponent)