https://file.aiquickdraw.com/mathbot/file/17260383805381avgk1u2.jpg

I see the image you uploaded contains a set of math exercises in what appears to be a test format. Let me interpret the contents and solve the problems.

### Section 1
#### 1) 
\[
\frac{2^{11} \cdot 3^{11}}{6^5} \cdot \left(\frac{7}{4}\right)^0
\]
#### 2)
\[
(1.7 - 3.4) \cdot 6.12 - 3 \cdot 2^3
\]

### Section 2
#### 1)
\[
24(x^2 - 1) - (6x - 1)(4x + 1)
\]
#### 2)
\[
(4a - 1)(6b + 1) - 3a(8b + 2)
\]

### Section 3
#### 1)
\[
x^5y - y^5x + x^2z - y^2z
\]
#### 2)
\[
7a^{20} - a^{15} - 7a^{10} + a^5
\]

### Section 4
#### 1)
\[
\frac{(2x + 1)(2x - 3)}{4} = x^2 - 1
\]
#### 2)
\[
12x(x - 5) - (6x + 1)(2x - 3) = 47
\]

I'll now proceed to solve each of these step by step.

---

### Solutions

#### Section 1, Problem 1
First, simplify the expression:
\[
\left(\frac{7}{4}\right)^0 = 1
\]
Thus, the original expression simplifies to:
\[
\frac{2^{11} \cdot 3^{11}}{6^5}
\]
We know:
\[
6 = 2 \cdot 3, \quad \therefore 6^5 = (2 \cdot 3)^5 = 2^5 \cdot 3^5
\]
Substitute:
\[
\frac{2^{11} \cdot 3^{11}}{2^5 \cdot 3^5} = 2^{11-5} \cdot 3^{11-5} = 2^6 \cdot 3^6
\]
Finally:
\[
2^6 = 64, \quad 3^6 = 729, \quad 64 \cdot 729 = 46656
\]
So, the answer is **46656**.

#### Section 1, Problem 2
Simplify:
\[
(1.7 - 3.4) = -1.7
\]
Now the expression becomes:
\[
-1.7 \cdot 6.12 - 3 \cdot 2^3
\]
First, compute powers and multiplication:
\[
2^3 = 8, \quad 3 \cdot 8 = 24
\]
Next:
\[
-1.7 \cdot 6.12 = -10.404
\]
So the final expression is:
\[
-10.404 - 24 = -34.404
\]
Answer: **-34.404**

#### Section 2, Problem 1
Expand and simplify:
\[
24(x^2 - 1) = 24x^2 - 24
\]
Expand the second part:
\[
(6x - 1)(4x + 1) = 24x^2 + 6x - 4x - 1 = 24x^2 + 2x - 1
\]
Subtract:
\[
24x^2 - 24 - (24x^2 + 2x - 1) = 24x^2 - 24 - 24x^2 - 2x + 1
\]
Simplify:
\[
-24 - 2x + 1 = -2x - 23
\]
Answer: **-2x - 23**

---

Would you like me to continue with the next problems or explain further? 

Here are 5 related questions you might find helpful:
1. How do you handle fractional exponents?
2. What are the key rules for expanding binomials?
3. How does exponentiation of zero simplify expressions?
4. What are some common mistakes in solving polynomials?
5. How do you apply factorization techniques to solve algebraic equations?

**Tip:** Always simplify inside parentheses first when dealing with multiple operations.

The image contains a set of math problems, including algebraic expressions, simplifications, polynomial equations, and factorization tasks.

Solve algebraic expressions involving exponents, binomial expansions, and polynomial factorization. This test includes key concepts such as simplifying exponents, applying the distributive property, and solving quadratic equations. Suitable for Grades 8-10.

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