If `t^(3)=-8`, what is the value of `t^(2)`?

Options

A. `-4`
B. `-2`
C. `2`
D. `4`

Answer

To solve the equation \( t^3 = -8 \) and find the value of \( t^2 \), we can follow these steps:

### Step 1: Solve for \( t \)
We start with the equation:
\[ t^3 = -8 \]
To find \( t \), we take the cube root of both sides:
\[ t = \sqrt[3]{-8} \]
Since \(-8\) can be expressed as \(-2^3\), we have:
\[ t = -2 \]

### Step 2: Calculate \( t^2 \)
Now that we have the value of \( t \), we can find \( t^2 \):
\[ t^2 = (-2)^2 \]
Calculating this gives:
\[ t^2 = 4 \]

### Final Answer
Thus, the value of \( t^2 \) is:
\[ \boxed{4} \]

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