Question

Simplify: (8^2/3)^4​

Answer 1

In fraction form, it’s 213333^4/ 10,000^4

Answer 2

`(8^{(2)/(3) } )^(4) = 256`

Explanation:

Given

`(8^{(2)/(3) } )^(4)`

Required

Simplify

To simplify this, we apply law of indices but first we start by solving the expression in bracket.

8 =2 * 2 * 2

8 = 2³

So, we substitute 2³ for 8

`(8^{(2)/(3) } )^(4)` becomes

`((2^(3))^{(2)/(3) } )^(4)`

From law of indices

`a^(n) = (a^(m))^{(n)/(m) }` ==>
`(a^(m))^{(n)/(m) } = a^(n)`

So,
`(2^(3))^{(2)/(3) } = 2^(2)`

At this point we have

`((2^(3))^{(2)/(3) } )^(4)` =
`(2^(2))^(4)`

Also, from law of indices

`(a^(m))^(n) = a^(m.n)`

So,

`((2^(3))^{(2)/(3) } )^(4)` =
`(2^(2))^(4)`

`(2^(2))^(4) = 2^(2*4)`

`(2^(2))^(4) = 2^(8)`

`(2^(2))^(4) = 256`

Hence,

`(8^{(2)/(3) } )^(4) = 256`