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 \( -\frac{5 x}{y^{-4}} \)

Sure, let's go through each of the questions one by one to identify the correct answers and understand the reasoning behind them. --- ### **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)** \( \frac{8}{x} \) --- ### **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)** \( 64 x^{6} \) --- ### **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)** \( 5 x y^{4} \) --- Feel free to reach out if you have more questions or need further clarification on these topics!