Балл) Упростите выражение: 1. х⁶у⁷·х³у²:(х⁹у⁹)+1 а¹¹:(а¹¹:а⁶) б¹⁶·(б⁸:б⁶) (х⁵·х⁴):(х³·х²)

1. To simplify the expression:

2. х⁶у⁷·х³у²:(х⁹у⁹)+1

We can simplify it step by step:

First, let's simplify the numerator, х⁶у⁷·х³у²: х⁶ * х³ = х⁹ (we add the exponents when multiplying like bases) у⁷ * у² = у⁹ (same here)

So, the numerator simplifies to: х⁹у⁹

Now, let's simplify the denominator (х⁹у⁹) + 1: The denominator remains the same.

Putting it all together, the simplified expression is: (х⁹у⁹)/(х⁹у⁹ + 1)

2. а¹¹:(а¹¹:а⁶)

To simplify this expression: First, let's simplify the denominator, а¹¹:а⁶: а¹¹ / а⁶ = а⁵ (we subtract the exponents when dividing like bases)

Now, the simplified expression is: а⁵

3. б¹⁶·(б⁸:б⁶)

To simplify this expression: Let's simplify б⁸:б⁶: б⁸ / б⁶ = б² (we subtract the exponents when dividing like bases)

Now, the simplified expression is: б¹⁶·б²

4. (х⁵·х⁴):(х³·х²)

To simplify this expression: х⁵ * х⁴ = х⁹ (we add the exponents when multiplying like bases) х³ * х² = х⁵ (same here)

Now, (х⁵·х⁴):(х³·х²) simplifies to: х⁹/х⁵