Final answer:
To simplify (-2x³y⁻⁶)³, we raise each term inside the parentheses to the power of 3, simplifying it to -8x⁹y⁻¹⁸.
Step-by-step explanation:
To simplify the expression (-2x³y⁻⁶)³, we need to raise each term inside the parentheses to the power of 3. When we raise a power to another power, we multiply the exponents. So we have (-2x³)³ and (y⁻⁶)³. For the first term, (-2x³)³, we have (-2)³ * (x³)³. (-2)³ equals -8 and (x³)³ equals x⁹, so the first term simplifies to -8x⁹.
For the second term, (y⁻⁶)³, we have (y⁻⁶)³ = y⁻¹⁸. When we raise a negative exponent to another power, we change the sign of the exponent and make it positive. So y⁻⁶ raised to the power of 3 becomes y⁻¹⁸.
Putting it all together, the simplified expression is -8x⁹y⁻¹⁸.