Question

If \( xy \neq 0 \), which of the following is equivalent to \( \left(\frac{x}{y}\right)^3 \left(\frac{2x}{y}\right)^4 \)?

• A. \( 2xy \)
• B. \( 8xy^2 \)
• C. \( 16x^2 y^3 \)
• D. \( \frac{2y}{x} \)
• E. \( \frac{16y}{x} \)

Hint:

Check for expression errors.

Answer 1

Answer: (E)

Step 1: \( \left(\frac{x}{y}\right)^3 = \frac{x^3}{y^3} \).
Step 2: \( \left(\frac{2x}{y}\right)^4 = \frac{16x^4}{y^4} \).
Step 3: Multiply: \( \frac{x^3}{y^3} \times \frac{16x^4}{y^4} = \frac{16x^7}{y^7} \).
Step 4: No match; options suggest typo. If intended \( \left(\frac{2y}{x}\right)^4 \) or adjusted, (E) \( \frac{16y}{x} \) fits with misprint assumption.