https://file.aiquickdraw.com/mathbot/file/1726793072572kzqpaf36.jpg

I can see the math problems from the image you uploaded. Let's go through them one by one.

### Question 1:
Given \( x = -2 \), \( y = 2 \), and \( z = 3 \), solve:

\[
\frac{\left( xy^3 \right)^2 \cdot \left( yz^{-1} \right)^{-3}}{xy^2 z^2}
\]

### Question 2:
Simplify the expression:

\[
\frac{15x^5 yz^{12}}{5x^{-2}z^2}
\]

### Question 3:
Solve the expression:

\[
1000^0 + 100^0 + 10^0 + 1^0 + \left( \frac{1}{10} \right)^0
\]

### Question 4:
Find the value of:

\[
81^6 \times 9^5 \div 27^{10}
\]

### Question 5:
Calculate:

\[
125^{\frac{2}{3}} - 81^{\frac{3}{4}} + 36^{\frac{1}{2}}
\]

I'll begin by solving these step-by-step.Here are the solutions to the questions:

### Question 1:
The result of the expression \(\frac{\left( xy^3 \right)^2 \cdot \left( yz^{-1} \right)^{-3}}{xy^2 z^2}\) with \(x = -2\), \(y = 2\), and \(z = 3\) is:

\[
\boxed{-12}
\]

### Question 2:
The simplified form of \(\frac{15x^5 yz^{12}}{5x^{-2} z^2}\) is:

\[
\boxed{3x^7 yz^{10}}
\]

### Question 3:
The result of the expression \(1000^0 + 100^0 + 10^0 + 1^0 + \left(\frac{1}{10}\right)^0\) is:

\[
\boxed{5}
\]

### Question 4:
The value of \(81^6 \times 9^5 \div 27^{10}\) is:

\[
\boxed{81}
\]

### Question 5:
The result of the expression \(125^{\frac{2}{3}} - 81^{\frac{3}{4}} + 36^{\frac{1}{2}}\) is approximately:

\[
\boxed{4}
\]

Let me know if you need further details or explanations!

### Related Questions:
1. How do negative exponents affect the value of a fraction?
2. What is the property of any number raised to the power of 0?
3. How do you simplify expressions involving powers of products?
4. How do you handle fractional exponents when simplifying roots?
5. What is the best approach to solve mixed exponent expressions?

**Tip:** Always simplify powers step-by-step by following the order of operations (PEMDAS).

1. Diketahui x = -2, y = 2, dan z = 3 maka hasil dari (xy^3)^2 (yz^-1)^-3 / xy^2 z^2 adalah ... 
2. Bentuk sederhana dari 15x^5 yz^12 / 5x^-2 z^2 adalah ... 
3. Hasil dari 1000^0 + 100^0 + 10^0 + 1^0 + (1/10)^0 adalah ... 
4. Hasil dari 81^6 * 9^5 ÷ 27^10 adalah ... 
5. Hasil dari 125^(2/3) - 81^(3/4) + (36)^(1/2) adalah ...

This problem set involves solving complex algebraic expressions using exponentiation, simplification of powers, and properties of exponents, suitable for high school students in Grades 9-12. Detailed step-by-step solutions are provided for problems involving powers of zero, fractional exponents, and simplifying algebraic terms.

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