Sure! I'd be happy to explain how to simplify an expression with negative exponents using the rules for multiplying monomials.
To simplify an expression with negative exponents, we can use the following rules for multiplying monomials:
1. Rule of Product: When multiplying two monomials with the same base, we add the exponents.
For example: a^m * a^n = a^(m+n)
2. Rule of Quotient: When dividing two monomials with the same base, we subtract the exponent of the denominator from the exponent of the numerator.
For example: a^m / a^n = a^(m-n)
Now, let's go through an example step-by-step:
Example: Simplify the expression (3x^2) / (2y^-3)
Step 1: Apply the rules of exponents to simplify the expression within the parentheses:
- The exponent 2 applies to the variable 'x', so we keep it as it is.
- The exponent -3 applies to the variable 'y', but since it is negative, we move it to the denominator and change the sign to positive: y^-3 becomes y^3 in the denominator.
Step 2: Apply the rule of quotient to divide the monomials:
(3x^2) / (2y^3) = (3/2) * (x^2 / y^3)
Step 3: The expression is now simplified as (3/2) * (x^2 / y^3).
In summary, to simplify an expression with negative exponents using the rules for multiplying monomials, we first apply the rules of exponents to simplify the expression within parentheses. Then, we use the rule of quotient to perform the division if there are any negative exponents. Finally, we express the result as a fraction or a multiplication of monomials with positive exponents.