Solve [(4-2)²]³: A Triple Exponent Challenge

Question

[(42)2]3= [(4-2)^2]^3=

Video Solution

Solution Steps

00:06 Let's solve this math expression, step by step.
00:09 First, we always calculate what's inside the parentheses.
00:14 Next, we calculate the square of the number.
00:17 Now, let's break down the power and solve it.
00:21 Let's solve the first multiplication.
00:24 Break the number sixteen into ten plus six.
00:28 Open the parentheses, and multiply by each part.
00:33 Now, solve each multiplication, then add them together.
00:37 Great work! That's how you find the solution.

Step-by-Step Solution

To solve the expression [(42)2]3 [(4-2)^2]^3 , we need to follow the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction).

Step 1: Solve the innermost parentheses:

The expression inside the innermost parentheses is 424-2. We perform the subtraction:

42=24-2 = 2

Step 2: Apply the exponentiation:

Next, we take the result of the subtraction and apply the squaring operation ((2)2)((2)^2):

22=42^2 = 4

Step 3: Apply the outer exponentiation:

Finally, we take the result of the previous step and raise it to the power of 3:

43=644^3 = 64

Therefore, the value of the expression [(42)2]3 [(4-2)^2]^3 is 6464.

Answer

64