(5a%5E6b)%5E2.jpeg "(7a^2)(5a^6b)^2")
Simplifying the Expression (7a^2)(5a^6b)^2
In mathematics, simplifying expressions involves rewriting them in their most basic and compact form. Let's explore how to simplify the expression (7a^2)(5a^6b)^2.
Understanding the Properties
To simplify this expression, we need to understand the following properties:
- Power of a product: (ab)^n = a^n * b^n
- Power of a power: (a^m)^n = a^(m*n)
Step-by-Step Simplification
- Simplify the inner power: (5a^6b)^2 = 5^2 * (a^6)^2 * b^2 = 25a^12b^2
- Multiply the simplified inner power by the term outside: (7a^2)(25a^12b^2) = 7 * 25 * a^2 * a^12 * b^2
- Combine like terms: 175a^(2+12)b^2
- Simplify the exponents: 175a^14b^2
The Final Simplified Expression
Therefore, the simplified form of (7a^2)(5a^6b)^2 is 175a^14b^2.