Step-by-Step Explanation of Indexing the Expression 7xy times xy times 7y
To solve the expression 7xy × xy × 7y, we will follow these steps:
Step 1: Simplify Each Part of the Expression
First, let’s break down the expression:
- 7xy consists of 7, x, and y.
- xy consists of x and y.
- 7y consists of 7 and y.
Step 2: Group Similar Terms
Now, let’s rearrange and combine these terms:
- Combine the coefficients (numbers) and the variables.
- Combine all the coefficients first: 7 × 1 × 7.
- Then, group the x's: x^1 × x^1.
- Finally, group the y's: y^1 × y × y^1.
Step 3: Perform the Multiplication
Coefficients:
- Calculate: 7 × 1 × 7 = 49.
Variables:
- For x: x^1 × x^1 = x^(1+1) = x^2.
- For y: y^1 × y × y^1 = y^(1+1+1) = y^3.
Step 4: Combine Everything Together
Now, combine the simplified coefficients with the variables:
Final Result: 49x^2y^3
Conclusion
The expression 7xy × xy × 7y simplifies to 49x^2y^3. By following these steps—simplifying, grouping, multiplying, and combining—we can easily handle index expressions in algebra.