Simplify $(4 x^3 y^3)(2 x^2 y)$.

Multiply the coefficients: 4 × 2 = 8 .
Multiply the x terms: x 3 × x 2 = x 3 + 2 = x 5 .
Multiply the y terms: y 3 × y = y 3 + 1 = y 4 .
Combine the results to get the simplified expression: 8 x 5 y 4 ​ .

Explanation

Understanding the problem We are asked to simplify the expression ( 4 x 3 y 3 ) ( 2 x 2 y ) . This involves multiplying terms with coefficients and variables raised to certain powers. To simplify this, we will multiply the coefficients and then multiply the variables with the same base by adding their exponents.

Multiplying the coefficients First, we multiply the coefficients: 4 × 2 = 8 .

Multiplying the x terms Next, we multiply the terms with the variable x . We have x 3 × x 2 . According to the rules of exponents, when multiplying terms with the same base, we add the exponents: x 3 × x 2 = x 3 + 2 = x 5 .

Multiplying the y terms Now, we multiply the terms with the variable y . We have y 3 × y . Since y is the same as y 1 , we have y 3 × y = y 3 + 1 = y 4 .

Combining the results Finally, we combine all the results: 8 x 5 y 4 .

Final Answer Therefore, the simplified expression is 8 x 5 y 4 .


Examples
Understanding how to simplify expressions with exponents is crucial in many areas, such as calculating the area or volume of geometric shapes. For example, if you have a rectangular prism with length 2 x 2 , width 4 x 3 , and height y 4 , the volume would be ( 2 x 2 ) ( 4 x 3 ) ( y 4 ) = 8 x 5 y 4 . Simplifying expressions helps in determining the volume or area in terms of variables.

Answered by GinnyAnswer | 2025-07-08

The simplified expression of ( 4 x 3 y 3 ) ( 2 x 2 y ) is 8 x 5 y 4 , achieved by multiplying the coefficients and adding the exponents of like bases. This process involves multiplying the numbers, then using the rules of exponents for the variables. The final result is 8 x 5 y 4 .
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Answered by Anonymous | 2025-07-19