Compare Powers: Evaluating 16^8 vs 16^(2+6)

Q: Why do I need to simplify the exponent in parentheses first?

The order of operations requires you to evaluate parentheses first! In $ 16^{(2+6)} $, you must calculate $ 2+6=8 $ before applying the exponent rule.

Q: Are these expressions really the same?

Yes! $ 16^8 $ and $ 16^{(2+6)} $ are identical because $ 2+6=8 $. The parentheses don't change the value, just the order of operations.

Q: What if the numbers in parentheses were different?

Great question! If you had $ 16^{(3+4)} $ vs $ 16^8 $, then \( 16^7 . Always simplify first to compare correctly.

Q: Do I need to calculate the actual value of 16^8?

No! You only need to recognize that both expressions simplify to the same form: $ 16^8 $. Since they're identical, they must be equal.

Q: What's the difference between 16^(2+6) and 16^2 + 16^6?

Huge difference! $ 16^{(2+6)} = 16^8 $ but $ 16^2 + 16^6 $ means adding two separate powers. Parentheses in the exponent affect the power, not the operation.

Exponent Rules with Order of Operations

Which is larger?

$16^8\text{ }_{——}16^{(2+6)}$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:07 Let's find out which number is bigger.

00:13 We'll start by calculating the numbers step by step.

00:17 It looks like both values are the same.

00:20 And that's how we solve the problem!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Which is larger?

$16^8\text{ }_{——}16^{(2+6)}$

Step-by-step solution

The problem involves comparing $16^8$ and $16^{(2+6)}$ .

First, simplify the exponent in the second expression:

$16^{(2+6)} = 16^8$

This simplifies directly to $16^8$ , which is identical to the first expression, $16^8$ .

Since both expressions are equal after simplification, we conclude that:

The two expressions are equal, therefore $=$ .

Final Answer

$=$

Key Points to Remember

Essential concepts to master this topic

Rule: Always simplify expressions inside parentheses first, including exponents
Technique: Calculate $16^{(2+6)} = 16^8$ by evaluating the parentheses
Check: Both expressions equal $16^8$ so they are equal ✓

Common Mistakes

Avoid these frequent errors

Ignoring order of operations in exponents
Don't treat $16^{(2+6)}$ as separate operations = wrong comparison! This leads to confusion about which expression is larger. Always simplify what's in parentheses first: $2+6=8$ , then recognize both are $16^8$ .

Practice Quiz

Test your knowledge with interactive questions

$$ 11^2= $$

FAQ

Everything you need to know about this question

Why do I need to simplify the exponent in parentheses first?

The order of operations requires you to evaluate parentheses first! In $16^{(2+6)}$ , you must calculate $2+6=8$ before applying the exponent rule.

Are these expressions really the same?

Yes! $16^8$ and $16^{(2+6)}$ are identical because $2+6=8$ . The parentheses don't change the value, just the order of operations.

What if the numbers in parentheses were different?

Great question! If you had $16^{(3+4)}$ vs $16^8$ , then $16^7 < 16^8$ . Always simplify first to compare correctly.

Do I need to calculate the actual value of 16^8?

No! You only need to recognize that both expressions simplify to the same form: $16^8$ . Since they're identical, they must be equal.

What's the difference between 16^(2+6) and 16^2 + 16^6?

Huge difference! $16^{(2+6)} = 16^8$ but $16^2 + 16^6$ means adding two separate powers. Parentheses in the exponent affect the power, not the operation.

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