In this question we have to find the value of x .Therefore, the value of x is 3 for given equation [tex](8x-8)^{3/2} =64[/tex].
Given:
[tex](8x-8)^{3/2} =64[/tex]
We need to determined the value of x for given equation.
Now, solve the equation,
[tex](8x-8)^{3/2} =64[/tex]
Now, taking both side one third and solve it further,
[tex]\(8x-8)^{1/2} =64^{\frac{1}{3} }[/tex]
Now, taking both side square and calculate it.
[tex](8x-8)^{1/2} = 4[/tex]
Then, again taking both side square.
Therefore, we get,
[tex](8x -8) = 4^2\\(8x -8) = 16\\8x = 16 + 8\\8x = 24\\x = 3[/tex]
Therefore, the value of x is 3 for given equation [tex](8x-8)^{3/2} =64[/tex].
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