Simplifying Expressions with Exponents
This article will walk through the steps of simplifying the expression (2x^2y^3)(3x^1y^5). We'll use the rules of exponents to arrive at a simplified form.
Understanding the Rules of Exponents
The key to simplifying this expression lies in understanding the following rules of exponents:
 Product of powers: When multiplying exponents with the same base, add the powers.
 Example: x^m * x^n = x^(m+n)
 Quotient of powers: When dividing exponents with the same base, subtract the powers.
 Example: x^m / x^n = x^(mn)
 Power of a power: When raising a power to another power, multiply the powers.
 Example: (x^m)^n = x^(m*n)
 Negative exponent: A term with a negative exponent can be written as its reciprocal with a positive exponent.
 Example: x^n = 1/x^n
Simplifying the Expression
Now, let's apply these rules to our expression:

Separate the numerical coefficients and variables: (2x^2y^3)(3x^1y^5) = (2 * 3)(x^2 * x^1)(y^3 * y^5)

Apply the product of powers rule: (2 * 3)(x^2 * x^1)(y^3 * y^5) = 6x^(2+(1))y^(3+5)

Simplify: 6x^(2+(1))y^(3+5) = 6x^1y^2

Write the final simplified expression: 6x^1y^2 = 6xy^2
Conclusion
Therefore, the simplified form of the expression (2x^2y^3)(3x^1y^5) is 6xy^2. By applying the rules of exponents, we can effectively simplify complex expressions and express them in a more concise form.