6a⁸b⁸-3a⁶b⁶-a²b³ entre 3a²b³


We need to simplify the expression:

\[
\frac{6a^8b^8 - 3a^6b^6 - a^2b^3}{3a^2b^3}
\]

### Step 1: Break down the expression by dividing each term by \(3a^2b^3\):

\[
\frac{6a^8b^8}{3a^2b^3} - \frac{3a^6b^6}{3a^2b^3} - \frac{a^2b^3}{3a^2b^3}
\]

### Step 2: Simplify each term individually:

- First term: 
  \[
  \frac{6a^8b^8}{3a^2b^3} = 2a^{8-2}b^{8-3} = 2a^6b^5
  \]

- Second term: 
  \[
  \frac{3a^6b^6}{3a^2b^3} = a^{6-2}b^{6-3} = a^4b^3
  \]

- Third term:
  \[
  \frac{a^2b^3}{3a^2b^3} = \frac{1}{3}
  \]

### Step 3: Write the final simplified expression:
\[
2a^6b^5 - a^4b^3 - \frac{1}{3}
\]

This is the simplified form of the given expression.

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Do you want further details or have any questions about this?

Here are five related problems for practice:

1. Simplify \(\frac{9a^9b^6 - 3a^7b^4}{3a^3b^2}\).
2. Factor \(6a^8b^8 - 3a^6b^6 - a^2b^3\).
3. Simplify \(\frac{12a^5b^6 - 6a^3b^4 + 2ab^2}{2ab^2}\).
4. Expand and simplify \((a^2b^3)(3a^4b^5 - 2a^2b^2)\).
5. Simplify \(\frac{4a^{10}b^7 + 2a^8b^5 - a^2b^3}{2a^2b^3}\).

**Tip**: When simplifying expressions with exponents, remember to subtract exponents when dividing powers with the same base.

6a⁸b⁸ - 3a⁶b⁶ - a²b³ entre 3a²b³

Learn how to simplify the algebraic expression (6a⁸b⁸ - 3a⁶b⁶ - a²b³) / (3a²b³) step-by-step. This problem covers key concepts in algebra, including the use of exponent rules and simplifying terms. Suitable for students in Grades 9-11.

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