Question 337678
Another way of writting the cubed root is X^(-3)
So given:  {{{2*(192)^-3 + 24^-3}}}
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To remove numbers from under the radical, the number has to appear the number of times that the radical is raised to. For example {{{sqrt(4) = 4^-2}}} Now the radical is raised to the second power so in order to remove a number from under the radical, the number must be there twice.  Factor the 4. 4 = 2*2. Now rewrite the equation. {{{4^-2 = 2}}}
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So for your given equation, we need to first find the factors of 24 and 192.
Lets start with 24
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24/3 = 8
8/2 = 4
6/2 = 2
So the factors of 24 = 2*2*2*3.
Notice that the 2 shows up three times.
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Find the factors of 192.
192/8 = 24
Now we just found the factors of 24 and 8
24 = 2*2*2*3
8 = 2*2*2
So the factors of 192 = 2*2*2*3*2*2*2
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Rewrite the given equation
{{{2*(192)^-3 + 24^-3}}}
{{{2*(2*2*2*3*2*2*2
)^-3 + (2*2*2*3)^-3}}}
Since both parts are raised to the -3 degree, we can take out a number as long as it shows up 3 times.
{{{2*(2*2)*3^-3 + 2*3^-3}}}
Simplify
{{{8*3^-3 + 2*3^-3}}}
Simplify
{{{10*3^-3}}}