Decompose using exponents 735 base of eight

To decompose the number 735 in base 8 using exponents, we follow the steps below. 

### Step 1: Understanding the representation

The number 735 in base 8 can be written as a sum of powers of 8, since it represents:

\[
735_8 = 7 \times 8^2 + 3 \times 8^1 + 5 \times 8^0
\]

### Step 2: Break it down

We decompose each digit using exponents:

- The first digit, **7**, is in the \(8^2\) place.
- The second digit, **3**, is in the \(8^1\) place.
- The third digit, **5**, is in the \(8^0\) place.

So, this gives us the following expression:

\[
735_8 = 7 \times 8^2 + 3 \times 8^1 + 5 \times 8^0
\]

### Step 3: Simplify each term

- \( 7 \times 8^2 = 7 \times 64 = 448 \)
- \( 3 \times 8^1 = 3 \times 8 = 24 \)
- \( 5 \times 8^0 = 5 \times 1 = 5 \)

### Step 4: Final sum

Adding these together:

\[
735_8 = 448 + 24 + 5 = 477_{10}
\]

Thus, the base-8 number \(735_8\) decomposes to \(7 \times 8^2 + 3 \times 8^1 + 5 \times 8^0\), which equals \(477_{10}\) in base 10.

Would you like more details on base conversions, or do you have any questions?

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Here are 5 related questions:

1. How do you convert a base-10 number back to base 8?
2. What is the process to convert other bases, like base 16 or base 2, into base 10?
3. How does base 8 compare to binary (base 2) in terms of practical applications?
4. What are the steps to convert a decimal fraction into base 8?
5. How can you quickly recognize whether a number is in base 8 from its

Explore the step-by-step process of decomposing the base-8 number 735 using exponents. This solution covers the breakdown of each digit in the base-8 number system, converting it into base-10 for easier understanding. Suitable for middle school students in Grades 6-8.

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