Sure, let's solve the expression [tex]\(\left(-\frac{2 x}{y^2}\right)^3\)[/tex] step-by-step.
1. Starting with the innermost part of the expression:
[tex]\[
-\frac{2x}{y^2}
\][/tex]
2. Since the exact values of [tex]\( x \)[/tex] and [tex]\( y \)[/tex] are not initially given, let's consider the provided numerical results to understand the handling:
We are given:
[tex]\[
\left(-\frac{2 \cdot 1}{1^2}\right)^3 = \left(-\frac{2 \cdot 1}{1}\right)^3 = (-2)^3
\][/tex]
3. First, calculate the intermediate result [tex]\(\left(-\frac{2x}{y^2}\right)\)[/tex]:
[tex]\[
-\frac{2 \cdot 1}{1^2} = -2
\][/tex]
4. Next, raise this intermediate result to the power of 3:
[tex]\[
(-2)^3 = (-2) \times (-2) \times (-2)
\][/tex]
5. Perform the multiplication:
[tex]\[
(-2) \times (-2) = 4
\][/tex]
[tex]\[
4 \times (-2) = -8
\][/tex]
6. Hence, the final result is:
[tex]\[
(-2)^3 = -8
\][/tex]
So the evaluated expression [tex]\(\left(-\frac{2 x}{y^2}\right)^3\)[/tex] yields the result [tex]\(-8\)[/tex] when [tex]\(x = 1\)[/tex] and [tex]\(y = 1\)[/tex].
