https://file.aiquickdraw.com/mathbot/file/1729378627871dwz3tuh6.jpg

Let's solve each of these expressions step-by-step. These involve using exponent rules for products, such as:

\[
(a \cdot b)^n = a^n \cdot b^n
\]

---

### 1. \((5x)^2\)  
\[
(5x)^2 = 5^2 \cdot x^2 = 25x^2
\]

### 2. \((4y)^3\)  
\[
(4y)^3 = 4^3 \cdot y^3 = 64y^3
\]

### 3. \((7ab)^2\)  
\[
(7ab)^2 = 7^2 \cdot a^2 \cdot b^2 = 49a^2b^2
\]

### 4. \((-2x)^3\)  
\[
(-2x)^3 = (-2)^3 \cdot x^3 = -8x^3
\]

### 5. \((-2x)^4\)  
\[
(-2x)^4 = (-2)^4 \cdot x^4 = 16x^4
\]

### 6. \((10ab)^4\)  
\[
(10ab)^4 = 10^4 \cdot a^4 \cdot b^4 = 10000a^4b^4
\]

### 7. \((6xyz)^2\)  
\[
(6xyz)^2 = 6^2 \cdot x^2 \cdot y^2 \cdot z^2 = 36x^2y^2z^2
\]

### 8. \((-xy)^5\)  
\[
(-xy)^5 = (-1)^5 \cdot x^5 \cdot y^5 = -x^5y^5
\]

### 9. \((7rs)^3\)  
\[
(7rs)^3 = 7^3 \cdot r^3 \cdot s^3 = 343r^3s^3
\]

### 10. \((5x)^{-2}\)  
\[
(5x)^{-2} = \frac{1}{(5x)^2} = \frac{1}{25x^2}
\]

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If you need further clarifications or additional explanations, feel free to ask!

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### Related Questions:
1. What happens when an exponent is zero?
2. How do negative exponents affect the expression?
3. What is the rule for raising a product to a power?
4. How do exponents apply to fractional bases?
5. What happens if an exponent is negative and the base includes a negative number?

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**Tip:** When raising a product to a power, apply the exponent to each factor individually to simplify the expression.

Simplify each of the following expressions: (5x)^2, (4y)^3, (7ab)^2, (-2x)^3, (-2x)^4, (10ab)^4, (6xyz)^2, (-xy)^5, (7rs)^3, (5x)^{-2}

Learn how to simplify expressions with exponents like (5x)^2, (4y)^3, and (7ab)^2 using exponent rules. This step-by-step guide covers key algebraic concepts such as applying powers to products and negative exponents. Suitable for Grades 7-9.

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