Solve the following equation.
\[
-27 x^{-3 / 4}=-64
\]
Select the correct response below and if there is more than one solution enter them in any order. Round to three dec places.
$x_{1}=$ or $x_{2}=$
$x_{1}=$
There is no solution.

Answer

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Answer

The solution to the equation is $x = \boxed{0.316}$.

Steps

Step 1 ：The given equation is $-27 x^{-3 / 4}=-64$.

Step 2 ：Divide both sides by $-27$ to isolate $x^{-3 / 4}$ on one side, we get $x^{-3 / 4} = \frac{-64}{-27} = 2.37$.

Step 3 ：Raise both sides to the power of $-4/3$ to solve for $x$, we get $x = (2.37)^{-4/3} = 0.316$.

Step 4 ：The solution to the equation is $x = \boxed{0.316}$.