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

Q: Why do I need to calculate 3×2×4 before squaring?

The parentheses tell you to do this multiplication first! $ (3×2×4)^2 $ means square the entire result of 24, not square each number separately.

Q: What's the difference between this and $ 3^2×2^2×4^2 $ ?

Huge difference! $ (3×2×4)^2 = 24^2 = 576 $, but $ 3^2×2^2×4^2 = 9×4×16 = 576 $. They happen to equal the same number here, but that's coincidental - the methods are totally different!

Q: How do I solve for y once I have 576 = 3y?

Divide both sides by 3! Think: what times 3 equals 576? The answer is $ y = \frac{576}{3} = 192 $.

Q: Can I use a calculator for $ 24^2 $ ?

Absolutely! But also try to recognize that $ 24^2 = (20+4)^2 $ or remember $ 24×24 $. Mental math helps build number sense!

Q: What if I get confused by the order of operations?

Use PEMDAS! Parentheses first (3×2×4=24), then Exponents ($ 24^2=576 $), finally solve the equation 576=3y.

Exponent Evaluation with Multi-Step Operations

Find the value of y:

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

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

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 written solution

Follow each step carefully to understand the complete solution

Understand the problem

Find the value of y:

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

Step-by-step solution

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

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

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

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

Final Answer

$y=192$

Key Points to Remember

Essential concepts to master this topic

Order: Parentheses first, then exponents, finally division for y
Technique: Calculate 3×2×4=24, then $24^2=576$
Check: Verify $3(192)=576$ matches $(24)^2$ ✓

Common Mistakes

Avoid these frequent errors

Squaring each factor separately before multiplying
Don't calculate $3^2×2^2×4^2=9×4×16=576$ directly! This skips the parentheses and gives the same numerical result by luck, but shows wrong understanding. Always evaluate inside parentheses completely first, then apply the exponent to that single result.

Practice Quiz

Test your knowledge with interactive questions

Choose the expression that corresponds to the following:

$$ $\left(2\times11\right)^5=$

FAQ

Everything you need to know about this question

Why do I need to calculate 3×2×4 before squaring?

The parentheses tell you to do this multiplication first! $(3×2×4)^2$ means square the entire result of 24, not square each number separately.

What's the difference between this and $3^2×2^2×4^2$ ?

Huge difference! $(3×2×4)^2 = 24^2 = 576$ , but $3^2×2^2×4^2 = 9×4×16 = 576$ . They happen to equal the same number here, but that's coincidental - the methods are totally different!

How do I solve for y once I have 576 = 3y?

Divide both sides by 3! Think: what times 3 equals 576? The answer is $y = \frac{576}{3} = 192$ .

Can I use a calculator for $24^2$ ?

Absolutely! But also try to recognize that $24^2 = (20+4)^2$ or remember $24×24$ . Mental math helps build number sense!

What if I get confused by the order of operations?

Use PEMDAS! Parentheses first (3×2×4=24), then Exponents ( $24^2=576$ ), finally solve the equation 576=3y.

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

Exponent Evaluation with Multi-Step Operations

❤️ Continue Your Math Journey!

Step-by-step video solution

Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Key Points to Remember

Common Mistakes

Practice Quiz

FAQ

Why do I need to calculate 3×2×4 before squaring?

What's the difference between this and $3^2×2^2×4^2$ ?

How do I solve for y once I have 576 = 3y?

Can I use a calculator for $24^2$ ?

What if I get confused by the order of operations?

🌟 Unlock Your Math Potential

More Questions

Power of a Product

Expand (2a)^(y+5): Step-by-Step Expression Expansion

Complete the Expression: Writing (ax×3)^b in Standard Form

Evaluate the Complex Expression: 3⁹×12⁴×6⁹×4⁹×4⁴×7⁹

Reduce the Expression: 7⁶ × 13² × 4² × 8⁷ × 9² Using Laws of Exponents

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

Exponent Evaluation with Multi-Step Operations

❤️ Continue Your Math Journey!

Step-by-step video solution

Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Key Points to Remember

Common Mistakes

Practice Quiz

FAQ

Why do I need to calculate 3×2×4 before squaring?

What's the difference between this and 32×22×42 3^2×2^2×4^2 32×22×42?

How do I solve for y once I have 576 = 3y?

Can I use a calculator for 242 24^2 242?

What if I get confused by the order of operations?

🌟 Unlock Your Math Potential

More Questions

Power of a Product

Expand (2a)^(y+5): Step-by-Step Expression Expansion

Complete the Expression: Writing (ax×3)^b in Standard Form

Evaluate the Complex Expression: 3⁹×12⁴×6⁹×4⁹×4⁴×7⁹

Reduce the Expression: 7⁶ × 13² × 4² × 8⁷ × 9² Using Laws of Exponents

What's the difference between this and $3^2×2^2×4^2$ ?

Can I use a calculator for $24^2$ ?