Question

what is the numerator of this expression (16−12)^2+5(8+2^2)5^3−(1+4)^2

Answer 1

To find the numerator of the expression \((16 - 12)^2 + 5(8 + 2^2)5^3 - (1 + 4)^2\), we will calculate it step by step.

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

2. Now, compute \((4)^2\):
\[
(4)^2 = 16
\]

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

4. Add that result to \(8\):
\[
8 + 4 = 12
\]

5. Now, multiply \(5\) by that sum:
\[
5 \times 12 = 60
\]

6. Calculate \(5^3\):
\[
5^3 = 125
\]

7. Multiply \(60\) by \(125\):
\[
60 \times 125 = 7500
\]

8. Now, calculate \((1 + 4)^2\):
\[
1 + 4 = 5 \quad \text{and} \quad (5)^2 = 25
\]

9. Now combine these results:
\[
16 + 7500 - 25
\]

10. Calculate \(16 - 25\):
\[
16 - 25 = -9
\]

11. Finally, add that to \(7500\):
\[
7500 - 9 = 7491
\]

So, the final result of the expression is:
\[
\boxed{7491}
\]