Chapter 7, Problem 1CRE

To determine

(a)

To check: whether the given equation match with resultant equation or not.

Answer to Problem 1CRE

The expression $2^a{3}^b$ has no match.

Explanation of Solution

Given:

The given equation is $2^a{3}^b$

The resultant equations are:

$\text{i}{\text{.2}}^{ab}\text{;ii}{\text{.6}}^{a+b}\text{;iii}\text{.}{\left(\frac{2}{3}\right)}^{a-b}$

Calculation:

The given equation is in the simplest form $2^a{3}^b$ ,

Therefore, the expression has no match.

To determine

(b)

To check: whether the given equation match with resultant equation or not.

Answer to Problem 1CRE

The expression $\frac{2^a}{3^b}$ has no match.

Explanation of Solution

Given:

The given equation is $\frac{2^a}{3^b}$

The resultant equations are:

$\text{i}{\text{.2}}^{ab}\text{;ii}{\text{.6}}^{a+b}\text{;iii}\text{.}{\left(\frac{2}{3}\right)}^{a-b}$

Calculation:

The given equation is in the simplest form $\frac{2^a}{3^b}$ ,

Therefore, the expression has no match.

To determine

(c)

To check: whether the given equation match with resultant equation or not.

Answer to Problem 1CRE

The expression $2^a{3}^b$ has match with option (i).

Explanation of Solution

Given:

The given equation is ${\left(2^a\right)}^b$

The resultant equations are:

$\text{i}{\text{.2}}^{ab}\text{;ii}{\text{.6}}^{a+b}\text{;iii}\text{.}{\left(\frac{2}{3}\right)}^{a-b}$

Calculation:

The given expression is ${\left(2^a\right)}^b$ can be simplified as ${\text{2}}^{ab}$

Therefore, the expression ${\left(2^a\right)}^b$ has match with ${\text{2}}^{ab}$.

To determine

(d)

To check: whether the given equation match with resultant equation or not.

Answer to Problem 1CRE

The expression $2^{a-b}{3}^{b-a}$ has match with option (iii).

Explanation of Solution

Given:

The given equation is $2^{a-b}{3}^{b-a}$

The resultant equations are:

$\text{i}{\text{.2}}^{ab}\text{;ii}{\text{.6}}^{a+b}\text{;iii}\text{.}{\left(\frac{2}{3}\right)}^{a-b}$

Calculation:

The given expression $2^{a-b}{3}^{b-a}$ can be simplified as ${\left(\frac{2}{3}\right)}^{a-b}$

Therefore, the expression has $2^{a-b}{3}^{b-a}$ match with ${\left(\frac{2}{3}\right)}^{a-b}$.