Question

For m>0, the expression (in the image) can be rewritten in the form 2m^a, where a is a fraction. Then a=___

Answer 1

The calculated value of the variable a in the expression
`\frac{2(\sqrt m)^3}{\sqrt[4]{m}} = 2m^a\\` is 5/4

How to determine the value of the expression a

From the question, we have the following parameters that can be used in our computation:

`\frac{2(\sqrt m)^3}{\sqrt[4]{m}}`

Also, we have that this expression equals

`2m^a`

So, we have

`\frac{2(\sqrt m)^3}{\sqrt[4]{m}} = 2m^a\\`

Divide both sides of the equation by 2

`\frac{(\sqrt m)^3}{\sqrt[4]{m}} = m^a`

This gives

`(m^(3)/(2))/(m^(1)/(4)) = m^a`

Applying the law of indices, we have

`m^{(3)/(2) - (1)/(4)} = m^a`

So, we have

`a = (3)/(2) - (1)/(4)`

Take the LCM and evaluate

`a = (6 - 1)/(4)`

Evaluate

a = 5/4

Hence, the value of a in the expression is 5/4

Answer 2

From the question;

we need to simplify

`\frac{2(\sqrt[]{m})^3}{\sqrt[4]{m}}`

In the form

`2m^a`

solving

`\begin{gathered} \frac{2(\sqrt[]{m})^3}{\sqrt[4]{m}} \\ =\text{ }\frac{2(m^{(1)/(2)})^3}{m^{(1)/(4)}} \\ =\text{ }\frac{2m^{3\text{ }*(1)/(2)}}{m^{(1)/(4)}} \\ =\text{ }\frac{2m^{(3)/(2)}}{m^{(1)/(4)}} \\ \text{applying law of indices} \\ =2m^{(3)/(2)\text{ - }(1)/(4)} \\ =2m^{\frac{6\text{ - 1}}{4}} \\ =2m^{(5)/(4)} \end{gathered}`

comparing the result

`\begin{gathered} 2m^{(5)/(4)}=2m^a \\ \text{implies} \\ m^{(5)/(4)}=m^a \end{gathered}`

Hence,

The value of a is

`(5)/(4)`