Can anyone explain to me how to simplify an expression with negative exponents using the rules for multiplying monomials? Have to know it and im not sure!!
Thanks!!
Of course! Simplifying expressions with negative exponents using the rules for multiplying monomials involves applying the properties of exponents. Here's a step-by-step explanation:
Step 1: Identify any negative exponents in the expression.
Step 2: Apply the rule that states a negative exponent can be rewritten as the reciprocal of the base with a positive exponent. In other words, if you have a term with a negative exponent, move it to the denominator (or numerator, if it's in the denominator), and change the sign of the exponent to positive.
Step 3: Apply the rule for multiplying monomials, which states that when multiplying two monomials with the same base, you add their exponents.
Step 4: Simplify the expression by multiplying the coefficients (numbers) and combining the like terms (with the same variables and exponents).
Let's work through an example to illustrate these steps:
Example: Simplify the expression 5x^(-2) * 3x^(-3).
Step 1: Identify the negative exponents in the expression, which are -2 and -3.
Step 2: Apply the rule by moving the terms with negative exponents to the denominator and changing the sign of the exponents:
= 5/(x^2) * 3/(x^3)
Step 3: Apply the rule for multiplying monomials by adding the exponents:
= 5 * 3 / (x^(2+3))
= 15 / x^5
Step 4: Simplify the expression by multiplying the coefficients:
= 15 / x^5
This is the simplified expression with negative exponents using the rules for multiplying monomials.
I hope this helps! Let me know if you have any further questions.
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.
when multiplying, add exponents.
when dividing, subtract exponents.
x^5 * x^7 = x^12
x^-3 / x^-5 = x^(-3-(-5)) = x^(-3+5) = x^2
just take it a step at a time. Negative numbers are just like positive numbers. They add and subtract in the usual way.
Just remember that
1/x^n = x^-n
1/x^-n = x^n
moving a factor between numerator and denominator changes its sign.