To simplify the expression \( 136 \cdot 13 - 12 \), we can look at it step-by-step:
- First, recognize that \( 136 \) can also be expressed as \( 13^2 \) (since \( 13 \times 13 = 169 \) and \( 136 = 13 \times 10 + 6 \)).
- Rewrite \( 136 \cdot 13 \) as \( 13^2 \cdot 13 = 13^3 \).
- Therefore, we have \( 13^3 - 12 \).
Now let's evaluate this expression with the responses listed:
- Response A: \( 13 - 3 \) is not equivalent.
- Response B: \( 13^{\frac{11}{2}} \) is not equivalent.
- Response C: \( \frac{1}{13^3} \) is not equivalent.
- Response D: \( 13^3 \) is equivalent to part of our derived expression since it matches the \( 13^3 \) term.
Since none of the responses directly reflect the entire expression after simplification, let's analyze what we have.
If none are yet correct, but we can derive our own version (e.g. if we were actually computing the complete expression itself, like evaluating it more), we'd end with numeric expressions as they are presented.
The best-fit answer directly from your choices relating to parts of our expression is Response D: \( 13^3 \).
In summary, none of the options exactly simplify to \( 136 \cdot 13 - 12 \), but if you're looking for equivalent forms relating to components built from the simplified parts, (1 point) would lean on acknowledging components related to the full expression being \( 13^3 \) without \( -12 \).
Thus the correct response is \( \boxed{13^3} \).
1 answer