Evaluate a^-2/3 where a= 27 *show all work?

Answer 1

a^-2/3

Now the first thing to know is that when you have a negative power - it is the same as putting it in a fraction

i.e 1/a = a^-1

so

a^(-2/3) can be written as 1/(a^(2/3))

So putting a = 27

we have

1 / (27^(2/3))

Now any number to the power of 1/3 i.e x^(1/3) is the same as cubedroot(x)

Now the number '2' on the top, is treated as a 'squared'

so what you have is 1 / (cubed root(27^2))

if you can use your caluclator, you can work out that that is the same as

1/cuberoot(729)

=1/9

Hopefully thats the type of answer you are meant to be doing. Ask me if you get stuck.

Laura

So

y=27^-2/3

Now 27 = 3^3

So we have

y=(3^3)^-2/3

Now we can multiply both sides by 3 (this cancels out the /3 on the right hand side and you get)


=3^-2
=1/3^2
=1/9

Answer 2

27^1/3= cube root of 27=3. 27^2/3=3^2=9. 27^-2/3=1/9.

Answer 3

a^-2/3
=27^-2/3
=(3^3)^-2/3
3(-2)/3 = -2
=3^-2
=1/3^2
=1/9