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

Q: Why can't I just multiply the exponents 2 × 3?

The power rule $ (a^m)^n = a^{mn} $ only applies when you have the same base. Here we have $ [(4-2)^2]^3 $, where the base changes from (4-2) to 4 after the first exponent.

Q: What if I forgot to do the subtraction first?

Always follow PEMDAS! Parentheses come first, so you must calculate 4-2 = 2 before applying any exponents. Skipping this step will give you completely wrong answers.

Q: How do I keep track of all these steps?

Write each step clearly:Step 1: (4-2) = 2Step 2: [2²] = [4]Step 3: [4]³ = 64This prevents confusion and helps you catch mistakes!

Q: What's the difference between [2²]³ and 2^(2×3)?

$ [2^2]^3 = [4]^3 = 64 $ (nested operations), while $ 2^{2×3} = 2^6 = 64 $ (power rule). They happen to equal the same here, but this is not always true!

Order of Operations with Nested Exponents

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

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

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 written solution

Follow each step carefully to understand the complete solution

Understand the problem

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

Step-by-step solution

To solve the expression $[(4-2)^2]^3$ , 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 $4-2$ . We perform the subtraction:

$4-2 = 2$

Step 2: Apply the exponentiation:

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

$2^2 = 4$

Step 3: Apply the outer exponentiation:

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

$4^3 = 64$

Therefore, the value of the expression $[(4-2)^2]^3$ is $64$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

PEMDAS Rule: Work inside parentheses first, then exponents from inside out
Technique: Calculate (4-2) = 2, then 2² = 4, finally 4³ = 64
Check: Verify each step: 2 × 2 = 4, then 4 × 4 × 4 = 64 ✓

Common Mistakes

Avoid these frequent errors

Applying exponents in wrong order
Don't calculate [(4-2)²]³ as (4-2)^(2×3) = 2⁶ = 64! This treats it like a power rule instead of nested operations. Always work from innermost parentheses outward: first (4-2)² = 4, then [4]³ = 64.

Practice Quiz

Test your knowledge with interactive questions

$20\div(4+1)-3=$

FAQ

Everything you need to know about this question

Why can't I just multiply the exponents 2 × 3?

The power rule $(a^m)^n = a^{mn}$ only applies when you have the same base. Here we have $[(4-2)^2]^3$ , where the base changes from (4-2) to 4 after the first exponent.

What if I forgot to do the subtraction first?

Always follow PEMDAS! Parentheses come first, so you must calculate 4-2 = 2 before applying any exponents. Skipping this step will give you completely wrong answers.

How do I keep track of all these steps?

Write each step clearly:

Step 1: (4-2) = 2
Step 2: [2²] = [4]
Step 3: [4]³ = 64

This prevents confusion and helps you catch mistakes!

Is there a shortcut for nested exponents?

No safe shortcuts exist! Each set of brackets must be calculated separately. Trying to skip steps often leads to errors. Work systematically from innermost to outermost operations.

What's the difference between [2²]³ and 2^(2×3)?

$[2^2]^3 = [4]^3 = 64$ (nested operations), while $2^{2×3} = 2^6 = 64$ (power rule). They happen to equal the same here, but this is not always true!

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

Order of Operations with Nested Exponents

❤️ 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 can't I just multiply the exponents 2 × 3?

What if I forgot to do the subtraction first?

How do I keep track of all these steps?

Is there a shortcut for nested exponents?

What's the difference between [2²]³ and 2^(2×3)?

🌟 Unlock Your Math Potential

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