Simplifying Expressions with Exponents
This article will guide you through the process of simplifying the expression (5a^6b^4)(2a^3b). We will break down the steps involved using the rules of exponents.
Understanding the Rules
To simplify expressions with exponents, we need to recall the following key rules:
 Product of Powers: When multiplying powers with the same base, add the exponents. a^m * a^n = a^(m+n)
 Quotient of Powers: When dividing powers with the same base, subtract the exponents. a^m / a^n = a^(mn)
 Power of a Power: When raising a power to another power, multiply the exponents. (a^m)^n = a^(mn)*
 Negative Exponent: Any base raised to a negative exponent is equal to its reciprocal raised to the positive exponent. a^n = 1/a^n
Simplifying the Expression

Apply the Product of Powers Rule:
 (5a^6b^4)(2a^3b) = (5 * 2) * (a^6 * a^3) * (b^4 * b)
 = 10 * a^(6+3) * b^(4+1)

Simplify the exponents:
 = 10a^9b^3

Apply the Negative Exponent Rule:
 = 10a^9 * (1/b^3)

Combine the terms:
 = 10a^9 / b^3
Conclusion
Therefore, the simplified form of the expression (5a^6b^4)(2a^3b) is 10a^9 / b^3. Understanding the rules of exponents allows us to efficiently manipulate expressions and simplify them to their most basic form.