(5ab) Times (-2a^2b)^3

less than a minute read Jun 16, 2024

Simplifying the Expression (5ab) x (-2a^2b)^3

This article will guide you through the simplification of the expression (5ab) x (-2a^2b)^3. We'll break down the steps using the rules of exponents and multiplication.

Understanding the Exponent

The expression (-2a^2b)^3 means we multiply (-2a^2b) by itself three times.

Applying the Exponent Rule

We can distribute the exponent to each factor within the parentheses:

(-2a^2b)^3 = (-2)^3 * (a^2)^3 * (b)^3

Remember that when raising a power to another power, we multiply the exponents:

(-2)^3 * (a^2)^3 * (b)^3 = -8 * a^6 * b^3

Multiplication

Now we can multiply the results from the previous step with the first term (5ab):

(5ab) * (-8a^6b^3) = -40a^7b^4

Final Answer

Therefore, the simplified form of the expression (5ab) x (-2a^2b)^3 is -40a^7b^4.