$(3 x^2 \cdot 2 x^2)^2$
Answer (1)
First, multiply the terms inside the parenthesis: 3 x 2 × 2 x 2 = 6 x 4 .
Then, square the result: ( 6 x 4 ) 2 = 36 x 8 .
The simplified expression is 36 x 8 .
Explanation
Initial Expression Let's simplify the given expression step by step. We have the expression ( 3 x 2 × 2 x 2 ) 2 .
Simplifying Inside Parentheses First, we simplify the expression inside the parentheses. We multiply the coefficients and add the exponents of x :
3 x 2 × 2 x 2 = ( 3 × 2 ) × ( x 2 × x 2 ) = 6 x 2 + 2 = 6 x 4
Squaring the Expression Now, we square the resulting expression: ( 6 x 4 ) 2 = 6 2 × ( x 4 ) 2 = 36 x 4 × 2 = 36 x 8
Final Result Therefore, the simplified expression is 36 x 8 .
Examples
Understanding how to simplify expressions with exponents is crucial in various fields, such as physics and engineering. For instance, when calculating the area of a square with side length 3 x 2 × 2 x 2 , you would need to simplify this expression. The simplified area would be 36 x 8 , demonstrating a practical application of simplifying expressions with exponents.
