(3ab%5E5).jpeg "(2ab)(3ab^5)")
Simplifying the Expression (2ab)(3ab^5)
This article will guide you through simplifying the expression (2ab)(3ab^5).
Understanding the Basics
The expression involves multiplying two terms together. Let's break down each part:
- (2ab): This is a monomial containing a numerical coefficient (2), and two variables (a and b), each with an exponent of 1.
- (3ab^5): This is another monomial with a coefficient of 3, the variable 'a' with an exponent of 1, and the variable 'b' with an exponent of 5.
Applying the Rules of Exponents
To simplify the expression, we use the following rules of exponents:
- Product of powers: When multiplying exponents with the same base, add the powers. For example, x^m * x^n = x^(m+n)
- Commutative Property: The order in which we multiply numbers doesn't change the result. For example, a * b = b * a
Simplifying the Expression
- Multiply the coefficients: 2 * 3 = 6
- Multiply the 'a' variables: a^1 * a^1 = a^(1+1) = a^2
- Multiply the 'b' variables: b^1 * b^5 = b^(1+5) = b^6
Final Result
Putting it all together, the simplified form of (2ab)(3ab^5) is 6a^2b^6.