Question

Simplify each expression, and eliminate any negative exponents. (8x³y²)(3y³)

Answer 1

To simplify (8x³y²)(3y³), multiply the numerical coefficients to get 24, then add exponents of like bases to obtain x³ and y⁵. The simplified expression is 24x³y⁵.

Step-by-step explanation:

To simplify the expression (8x³y²)(3y³), we need to apply the rules of multiplication of exponentials. First, we multiply the numerical coefficients 8 and 3, and then we add the exponents of like bases (in this case, x and y) keeping in mind that when bases are multiplied, their exponents are added.

First step is to multiply the numerical coefficients:

• 8 * 3 = 24

Next, we combine the variables with their corresponding exponents:

• x³ remains unchanged as there is no x term in the second bracket, so we have x³
• y² * y³ = y⁵ (since 2 + 3 = 5)

So, (8x³y²)(3y³) = 24x³y⁵.