$$ .10 ightarrow 8 $$ HW Score: $$ 10.64 \%, 10 $$ of 94 points $$ \begin{array}{l}(7 y)^{9} \cdot(7 y)^{2}-7 y^{11} \ ( ext { Type exponential notation with positive exponents.) }\end{array} $$

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$$ .10 ightarrow 8 $$ HW Score: $$ 10.64 \%, 10 $$ of 94 points $$ \begin{array}{l}(7 y)^{9} \cdot(7 y)^{2}-7 y^{11} \ (	ext { Type exponential notation with positive exponents.) }\end{array} $$

UpStudy AI · Accepted Answer

To simplify the expression $$(7y)^9 \cdot (7y)^2 - 7y^{11}$$ and express it using exponential notation with positive exponents, follow these steps:

1. **Expand the Multiplication:**

$$
   (7y)^9 \cdot (7y)^2 = 7^{9} \cdot y^{9} \cdot 7^{2} \cdot y^{2}
   $$

2. **Combine Like Bases by Adding the Exponents:**

$$
   7^{9} \cdot 7^{2} = 7^{9+2} = 7^{11}
   $$
   
   $$
   y^{9} \cdot y^{2} = y^{9+2} = y^{11}
   $$

So, the multiplication simplifies to:

$$
   7^{11} y^{11}
   $$

3. **Subtract the Second Term:**

$$
   7^{11} y^{11} - 7y^{11}
   $$

4. **Factor Out the Common Term $$7y^{11}$$:**

$$
   7y^{11} \left(7^{10} - 1\right)
   $$

Here's how:
   
   $$
   7^{11} y^{11} = 7 \cdot 7^{10} y^{11} = 7y^{11} \cdot 7^{10}
   $$
   
   $$
   7^{11} y^{11} - 7y^{11} = 7y^{11} \cdot 7^{10} - 7y^{11} = 7y^{11} (7^{10} - 1)
   $$

**Final Simplified Expression:**

$$
7y^{11} \left(7^{10} - 1\right)
$$

This expression uses exponential notation with all positive exponents, as required.
The simplified expression is $$7y^{11} \left(7^{10} - 1\right)$$.

HW Score: of 94 points

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