Simplify the following: $4\left(x^4\right)\left(3 x^2\right)$ = ?
Answer (1)
Multiply the constants: 4 × 3 = 12 .
Multiply the variables using the exponent rule x a × x b = x a + b : x 4 × x 2 = x 4 + 2 = x 6 .
Combine the results: 12 × x 6 = 12 x 6 .
The simplified expression is 12 x 6 .
Explanation
Understanding the Expression We are asked to simplify the expression 4 ( x 4 ) ( 3 x 2 ) . This involves multiplying constants and variables with exponents. We will use the associative property of multiplication to rearrange and group like terms together.
Multiplying Constants First, we multiply the constants: 4 × 3 = 12 .
Multiplying Variables Next, we multiply the variable terms. Recall the exponent rule: x a × x b = x a + b . Therefore, x 4 × x 2 = x 4 + 2 = x 6 .
Combining Results Finally, we combine the results to get the simplified expression: 12 x 6 .
Examples
Understanding how to simplify expressions with exponents is crucial in many areas, such as physics and engineering. For example, when calculating the area of a square with side length 2 x 3 , you would square the side length to get ( 2 x 3 ) 2 = 4 x 6 . This skill is also essential in computer graphics, where transformations and scaling of objects often involve manipulating expressions with exponents.
