Solve open parentheses square root of 6 close parentheses to the 8 x power = 216x - 3.

Solution:

Given, open parentheses square root of 6 close parentheses to the 8 x power = 216x - 3.

The equation can be written as (√6)^8x = 216^{(x - 3)}

\((\sqrt{6})^{8x}=(6^{1/2})^{8x}\)

\((\sqrt{6})^{8x}=(6)^{4x}\)

Similarly, 216 = 6³

\((216)^{(x-3)}=(6^{^{3}})^{(x-3)}\)

\((216)^{(x-3)}=(6)^{3x-9}\)

Equating with same base,

\((6)^{4x}=(6)^{(3x-9)}\)

Now, 4x = 3x - 9

4x - 3x = -9

x = -9

Therefore, the value of x is -9.

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Solve open parentheses square root of 6 close parentheses to the 8 x power = 216x - 3.

Summary:

The solution of open parentheses square root of 6 close parentheses to the 8 x power = 216x - 3 is -9.