Solve (4×2)² : Order of Operations with Squares

Question

Insert the corresponding expression:

(4×2)2= \left(4\times2\right)^2=

Video Solution

Solution Steps

00:00 Simply
00:03 To open parentheses with power over multiplication
00:07 Raise each factor to the power
00:10 We will use this formula in our exercise
00:14 And this is the solution to the question

Step-by-Step Solution

To solve the problem (4×2)2 \left(4\times2\right)^2, we need to apply the rule of exponents known as the "Power of a Product". This rule states that (ab)n=an×bn (ab)^n = a^n \times b^n .

Here, a=4 a = 4 , b=2 b = 2 , and n=2 n = 2 .

  • Step 1: Apply the "Power of a Product" rule: (4×2)2=42×22 \left(4 \times 2\right)^2 = 4^2 \times 2^2 .

Thus, the expression (4×2)2 \left(4\times2\right)^2 is equivalent to 42×22 4^2 \times 2^2 .

Answer

42×22 4^2\times2^2