(3a%5E5b%5E2)-7a%5E9b%5E8.jpeg "(10a^4b^6)(3a^5b^2)-7a^9b^8")
Simplifying the Expression: (10a^4b^6)(3a^5b^2) - 7a^9b^8
This expression involves multiplying and subtracting terms with exponents. To simplify it, we'll use the rules of exponents:
1. Multiplication of Terms with Exponents:
- When multiplying terms with the same base, add the exponents.
2. Subtraction of Terms with Exponents:
- You can only subtract terms with the same base and the same exponent.
Let's break down the simplification:
(10a^4b^6)(3a^5b^2)
- Multiply the coefficients: 10 * 3 = 30
- Multiply the variables: a^4 * a^5 = a^(4+5) = a^9
- Multiply the variables: b^6 * b^2 = b^(6+2) = b^8
This gives us: 30a^9b^8
Now, the full expression becomes: 30a^9b^8 - 7a^9b^8
Since both terms have the same base (a and b) and the same exponents (9 and 8), we can subtract their coefficients:
30a^9b^8 - 7a^9b^8 = 23a^9b^8
Therefore, the simplified expression is 23a^9b^8.