Simplify the expression below.
$(5 x)^2$
A. $5 x^2$
B. $10 x^2$
C. $25 x^2$
D. $52 x^2$
Answer (1)
Apply the power of a product rule: ( ab ) n = a n b n .
Calculate 5 2 = 25 .
Simplify the expression: ( 5 x ) 2 = 25 x 2 .
The correct answer is 25 x 2 .
Explanation
Understanding the expression We are asked to simplify the expression ( 5 x ) 2 . This means we need to apply the exponent to both the constant 5 and the variable x .
Applying the power of a product rule To simplify ( 5 x ) 2 , we use the power of a product rule, which states that ( ab ) n = a n b n . In our case, a = 5 , b = x , and n = 2 . So, we have ( 5 x ) 2 = 5 2 × x 2 .
Calculating the square of 5 Now, we calculate 5 2 , which is 5 × 5 = 25 . Therefore, ( 5 x ) 2 = 25 x 2 .
Selecting the correct answer Comparing our simplified expression 25 x 2 with the given answer choices, we see that it matches option C.
Examples
Understanding how to simplify expressions like ( 5 x ) 2 is useful in many areas, such as calculating the area of a square. For example, if the side of a square is 5 x , then the area of the square is ( 5 x ) 2 = 25 x 2 . This type of calculation is also fundamental in physics when dealing with quantities that scale with the square of a variable, such as kinetic energy or electrical power.
