Question

\frac{\left(16-12\right)^2+5\left(8+2^2\right)}{5^3-\left(1+4\right)^2} what is the numarater but simplifide

Answer 1

To simplify the numerator of the expression

\[
\frac{(16 - 12)^2 + 5(8 + 2^2)}{5^3 - (1 + 4)^2},
\]

we first simplify each part of the numerator:

1. Calculate \( (16 - 12) \):
\[
16 - 12 = 4.
\]

2. Now, calculate \( (16 - 12)^2 \):
\[
(4)^2 = 16.
\]

3. Next, we need to calculate \( 2^2 \):
\[
2^2 = 4.
\]

4. Now calculate \( 8 + 2^2 \):
\[
8 + 4 = 12.
\]

5. Then, multiply by 5:
\[
5(12) = 60.
\]

Now, combine these two results for the numerator:
\[
(16 - 12)^2 + 5(8 + 2^2) = 16 + 60 = 76.
\]

Thus, the simplified numerator is \( 76 \).