Chapter 1, Problem 1CRE

To determine

To match:( a)-(d) with (i),(ii) or (iii) if possible.

Answer to Problem 1CRE

$\left(c\right)\to \left(i\right),\left(d\right)\to \left(iii\right)$

Explanation of Solution

Calculation:

$\left(a\right)2^a{3}^b$ which cannot be simplified further hence none of the option can be matched.

$\left(b\right)\frac{2^a}{3^b}$ which cannot be simplified further hence none of the option can be matched.

$\left(c\right){\left(2^a\right)}^b$ which can be simplified as $2^{ab}$ further hence option (i) which is $2^{ab}$ is correct.

$\left(d\right)2^{a-b}{3}^{b-a}$ which can be simplified as $2^{a-b}{3}^{-\left(a-b\right)}={\left(\frac{2}{3}\right)}^{a-b}$ further hence option (iii) ${\left(\frac{2}{3}\right)}^{a-b}$ is correct.

Thus, $\left(c\right)\to \left(i\right),\left(d\right)\to \left(iii\right)$