Evaluate and Solve: Determining y in (3 x 2 x 4)² = 3y

Question

Find the value of y:

(3×2×4)2=3y \left(3\times2\times4\right)^2=3y

Video Solution

Solution Steps

00:00 Determine the value of Y
00:04 According to the laws of exponents, a product raised to a power (N)
00:08 equals the product where each factor is raised to the same power (N)
00:11 We will apply this formula to our exercise
00:21 Let's break down the exponent into a product
00:28 Isolate Y
00:35 Calculate each exponent separately
00:41 Calculate the product
00:47 Break down 12 into 10 + 2
00:54 Open the parentheses properly, multiply by each factor
00:59 Combine and calculate in order to determine the solution
01:08 This is the solution

Step-by-Step Solution

To solve this problem, we'll follow these steps:

  • Step 1: Evaluate the expression inside the parentheses (3×2×4) (3 \times 2 \times 4) .
  • Step 2: Square the result from Step 1.
  • Step 3: Set the squared result equal to 3y 3y and solve for y y .

Now, let's work through each step:
Step 1: First, calculate 3×2=6 3 \times 2 = 6 .
Then multiply by 4: 6×4=24 6 \times 4 = 24 .
Step 2: Square the result: 242=576 24^2 = 576 .
Step 3: Set the equation 576=3y 576 = 3y .
To find y y , divide both sides by 3:
y=5763=192 y = \frac{576}{3} = 192 .

Therefore, the solution to the problem is y=192 y = 192 .

Answer

y=192 y=192