Question: Simplify. \( \left( \frac{b^4}{-2a^3} \right)^5 \) Write your answer without parentheses.

Simplify. \( \left( \frac{b^4}{-2a^3} \right)^5 \) Write your answer without parentheses.

Solution

Simplify the expression: \[ \left( \frac{b^4}{-2a^3} \right)^5 \] Start by applying the power of a quotient rule: \[ \left( \frac{b^4}{-2a^3} \right)^5 = \frac{(b^4)^5}{(-2a^3)^5} \] Simplify the numerator: \[ (b^4)^5 = b^{4 \times 5} = b^{20} \] Simplify the denominator: \[ (-2a^3)^5 = (-2)^5 (a^3)^5 = -32a^{3 \times 5} = -32a^{15} \] Combine the results: \[ \frac{b^{20}}{-32a^{15}} \] Final simplified answer is: \[ -\frac{b^{20}}{32a^{15}} \]