Question

onsider the expression: (16−12)^2+5(8+2^2)/5^3−(1+4)^2
(1 point)

Answer 1

Let's simplify the expression step by step:

The expression is:

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

1. **Calculate \( (16 - 12)^2 \)**:
\[
16 - 12 = 4 \\
(4)^2 = 16
\]

2. **Calculate \( 2^2 \)**:
\[
2^2 = 4
\]

3. **Now, substitute \( 2^2 \) in the expression \( 8 + 2^2 \)**:
\[
8 + 4 = 12
\]

4. **Calculate \( 5(8 + 2^2) \)**:
\[
5 \times 12 = 60
\]

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

6. **Now compute \( \frac{5(8 + 2^2)}{5^3} \)**:
\[
\frac{60}{125} = \frac{12}{25}
\]

7. **Calculate \( (1 + 4)^2 \)**:
\[
1 + 4 = 5 \\
(5)^2 = 25
\]

Now we can put all these values back into the main expression:

\[
16 + \frac{12}{25} - 25
\]

Next, we need a common denominator to combine the fractions. The common denominator is 25.

1. **Convert 16 to have a denominator of 25**:
\[
16 = \frac{16 \times 25}{25} = \frac{400}{25}
\]

2. **Convert 25 to have a denominator of 25**:
\[
25 = \frac{25 \times 25}{25} = \frac{625}{25}
\]

Combining all of these:

\[
\frac{400}{25} + \frac{12}{25} - \frac{625}{25}
\]

Combine these fractions:

\[
\frac{400 + 12 - 625}{25} = \frac{-213}{25}
\]

Thus, the final simplified value of the expression is:

\[
\boxed{-\frac{213}{25}} \text{ or } -8.52
\]