1/17/25, 8:30 AM Simplify $$ 8 x^{-1} $$ A $$ \frac{8}{x} $$ B $$ \frac{1}{8 x} $$ C $$ -8 x $$ D QUESTION 29 Simplify $$ \left(4 x^{2}\right)^{3} $$ A $$ 4 x^{6} $$ B $$ 64 x^{6} $$ c $$ 4 x^{5} $$ D $$ 12 x^{6} $$ QUESTION 30 $$ -\frac{5 y^{4}}{-x^{-1}} $$ A $$ -\frac{5 x}{y 4} $$ B $$ \frac{x}{5 y^{\prime}} $$ C $$ 5 x y^{4} $$ D $$ -\frac{5 x}{y^{-4}} $$

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Sure, let's go through each of the questions one by one to identify the correct answers and understand the reasoning behind them.

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### **QUESTION 28**

**Simplify:**
$$ 8 x^{-1} $$

**Options:**
- **A)** $$ \frac{8}{x} $$
- **B)** $$ \frac{1}{8x} $$
- **C)** $$ -8 x $$
- **D)** *(No option provided)*

**Solution:**
The expression $$ x^{-1} $$ is equivalent to $$ \frac{1}{x} $$. Therefore:
$$
8 x^{-1} = 8 \times \frac{1}{x} = \frac{8}{x}
$$

**Answer:**
**A)** $$ \frac{8}{x} $$

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### **QUESTION 29**

**Simplify:**
$$
\left(4 x^{2}\right)^{3}
$$

**Options:**
- **A)** $$ 4 x^{6} $$
- **B)** $$ 64 x^{6} $$
- **C)** $$ 4 x^{5} $$
- **D)** $$ 12 x^{6} $$

**Solution:**
When raising a product to a power, apply the exponent to both the coefficient and the variable:
$$
\left(4 x^{2}\right)^{3} = 4^{3} \times \left(x^{2}\right)^{3} = 64 \times x^{6} = 64 x^{6}
$$

**Answer:**
**B)** $$ 64 x^{6} $$

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### **QUESTION 30**

**Simplify:**
$$
-\frac{5 y^{4}}{-x^{-1}}
$$

**Options:**
- **A)** $$ -\frac{5 x}{y^4} $$
- **B)** $$ \frac{x}{5 y} $$ *(Assuming the apostrophe in $$ y' $$ is a typo)*
- **C)** $$ 5 x y^{4} $$
- **D)** $$ -\frac{5 x}{y^{-4}} $$

**Solution:**
First, simplify the negative signs:
$$
-\frac{5 y^{4}}{-x^{-1}} = \frac{5 y^{4}}{x^{-1}}
$$
Recall that $$ x^{-1} = \frac{1}{x} $$. Therefore:
$$
\frac{5 y^{4}}{x^{-1}} = 5 y^{4} \times x = 5 x y^{4}
$$

**Answer:**
**C)** $$ 5 x y^{4} $$

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Feel free to reach out if you have more questions or need further clarification on these topics!
**Simplify the following expressions:** 1. **Question 28:** $$ 8 x^{-1} = \frac{8}{x} $$ - **Answer:** A) $$ \frac{8}{x} $$ 2. **Question 29:** $$ \left(4 x^{2}\right)^{3} = 64 x^{6} $$ - **Answer:** B) $$ 64 x^{6} $$ 3. **Question 30:** $$ -\frac{5 y^{4}}{-x^{-1}} = 5 x y^{4} $$ - **Answer:** C) $$ 5 x y^{4} $$

1/17/25, 8:30 AM
Simplify

A

B

C

D

QUESTION 29

Simplify

A

B
c

D

QUESTION 30

A

B

C

D

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Solución

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1/17/25, 8:30 AM Simplify A B C D QUESTION 29 Simplify A B c D QUESTION 30 A B C D