Question #06afa

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Answer 1 · 2017-06-19T00:27:51

In case of exponents, you can rewrite it as a radical and simplify it from there. In this case, it is #16#.

In a radical format, #8^(4/3)# can be rewritten as a #root(3)(8^4)# or as #(root(3)(8))^4#. I'll do both ways.

First method: #root(3)(8^4)#.

We would have to evaluate #8^4#.

#root(3)(8^4)#

#=root(3)(4096)#

Now we find the cube root of 4096.

#=root(3)(4096)#

#=16#

It just so happens that it is a whole number (which is very convenient).

The second method: #(root(3)(8))^4#.

With #(root(3)(8))^4#, we find the cube root of #8#, then you quart it.

#(root(3)(8))^4#

#=2^4#

#=16#

Therefore, the simplified version of #8^(4/3)# is #16#.

Hope this helps :)