How do you write #8^(4/3)# in radical form?
See a solution process below:
First, rewrite the expression as:
Next, use this rule of exponents to rewrite the expression again:
Now, use this rule for exponents and radicals to write this in radical form:
If necessary, we can reduce this further by first rewriting the radical as:
We can then use this rule for multiplying radicals to simplify the radical:
The denominator of the exponent tells us the root and the numerator tells us the power.
One way to recall which is which is to think about
This exponent is a reduced fraction.
If the fraction exponent is already reduced the it doesn't matter what order we use.
In fact, in the second for, if we notice that we know
I've tried to show the thought process. It would be fine to write just
We could also simplify
(We'd better be able to. I just said they are the same.)
# = root(3)(8^3) root(3)8#
# = 8root(3)8#
# = 8*2#
# = 16#