https://file.aiquickdraw.com/mathbot/file/1726230930083skvfz9xf.jpg

Let's break down and solve each of the problems in the image:

### 1. **If \( f(x) = -x^2 - x - 1 \), then what is \( f(-2) \)?**

We need to substitute \( x = -2 \) into the given function:
\[
f(x) = -x^2 - x - 1
\]
Substitute \( x = -2 \):
\[
f(-2) = -(-2)^2 - (-2) - 1
\]
\[
f(-2) = -(4) + 2 - 1
\]
\[
f(-2) = -4 + 2 - 1 = -3
\]
So, \( f(-2) = -3 \).

### 2. **True or False: \( 3^5 \cdot 3^2 = 3^{10} \)?**

Using the property of exponents \( a^m \cdot a^n = a^{m+n} \), we can simplify the left-hand side:
\[
3^5 \cdot 3^2 = 3^{5+2} = 3^7
\]
The right-hand side is \( 3^{10} \), and since \( 3^7 \neq 3^{10} \), the statement is **false**.

### 3. **True or False: \( \frac{(x^2)^3}{(x^2)(x^3)} = x \)?**

First, simplify the numerator and denominator:
\[
(x^2)^3 = x^{2 \cdot 3} = x^6
\]
Now, rewrite the expression:
\[
\frac{x^6}{x^2 \cdot x^3} = \frac{x^6}{x^{2+3}} = \frac{x^6}{x^5}
\]
Using the property \( \frac{a^m}{a^n} = a^{m-n} \), we simplify:
\[
\frac{x^6}{x^5} = x^{6-5} = x^1 = x
\]
So, the statement is **true**.

### 4. **Simplify the

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