Easy exponential question-> 1/3(8)^(-2/3)

[nukeman]

Easy exponential question---> 1/3(8)^(-2/3)

Homework Statement

I am doing a linear approximation question, and got stuck here with this simple stuff.

1/3(8)^(-2/3)

Can anyone explain what I need to do to turn the above into 1/12 ?

Homework Equations

The Attempt at a Solution

 

[BloodyFrozen]

Homework Statement

I am doing a linear approximation question, and got stuck here with this simple stuff.

1/3(8)^(-2/3)

Can anyone explain what I need to do to turn the above into 1/12 ?

Homework Equations

The Attempt at a Solution

$$8^{\frac{-2}{3}} = \frac{1}{8^{\frac{2}{3}}}$$

 

[Ray Vickson]

Homework Statement

I am doing a linear approximation question, and got stuck here with this simple stuff.

1/3(8)^(-2/3)

Can anyone explain what I need to do to turn the above into 1/12 ?

Homework Equations

The Attempt at a Solution

What you have written reads as
$$\frac{1}{3} 8^{-2/3}.$$ Is that what you meant, or did you want
$$\frac{1}{3\, 8^{-2/3}}?$$
If you mean the first one you should use brackets, like this: (1/3) 8^(-2/3), but if you mean the second one you should write 1/(8 2^(-2/3)).

RGV

 

[HallsofIvy]

As BloodyFrozen said, 8^-2/3= 1/8^2/3. Further, since 2³= 8, 8^1/3= 2 and so 8^2/3= 2²= 4.