Question

how do you do the quotient rule of exponent

Answer 1

[AI-generated answer — Bot GPT 3.5]

To use the quotient rule of exponents, follow these steps:

1. Identify the exponents in the equation or expression that you want to simplify.
For example, if you have an equation like x^m / x^n, the exponents here are "m" and "n".

2. Apply the quotient rule, which states that when you divide terms with the same base, you subtract the exponents.
In our example, you would apply the rule as x^m / x^n = x^(m - n).

3. Simplify the result if possible.
If the exponent in the denominator is greater than the exponent in the numerator (n > m), the quotient will result in x^(m - n) / 1. In this case, you can simplify the expression to 1 / x^(n - m) or x^(n - m) if the exponent difference is negative.

If the exponent in the numerator is greater than or equal to the exponent in the denominator (m ≥ n), the quotient will result in x^(m - n).

That's how you apply the quotient rule of exponents to simplify an equation or expression with exponents.

Answer 2

[AI-generated answer — Step-by-Step Bot]

The quotient rule for exponents allows us to simplify expressions where we divide two numbers or variables with exponents. The rule states that when dividing two exponential terms with the same base, you subtract the exponents.

Here are the steps to apply the quotient rule of exponents:

Step 1: Identify the base of the exponential terms. The base should be the same for both terms.
For example, consider the expression (a^m)/(a^n), the base here is 'a'.

Step 2: Subtract the exponent in the denominator from the exponent in the numerator.
Using the example above, subtract n from m: (a^m)/(a^n) = a^(m-n).

Step 3: Simplify the expression further if possible.
If the resulting exponent is positive, it remains in the numerator. If it's negative, it goes to the denominator.
Using our previous example, the final simplified expression would be a^(m-n).

Note: The quotient rule can also be applied to more complex expressions with multiple terms, as long as they have the same base. Just repeat steps 2 and 3 for each term.

Hope this helps!

Answer 3

[AI-generated answer — Explain Bot]

To understand and apply the quotient rule of exponents, follow these steps:

Step 1: Start by writing down the given expression involving exponents. For example, let's consider an expression like (a^m) / (a^n).

Step 2: Apply the quotient rule of exponents, which states that when dividing two numbers with the same base, you subtract the exponents. Using the example from Step 1, the quotient rule of exponents gives us:

(a^m) / (a^n) = a^(m - n).

Step 3: Simplify the expression further if possible. In the previous step, the expression was already simplified using the quotient rule. However, if you have any negative exponents, you can further simplify by applying the rule that a negative exponent is equivalent to taking the reciprocal of the positive exponent. For instance, if you have an expression like a^(-m), it can be rewritten as 1 / a^m.

That's it! You have successfully applied the quotient rule of exponents. Remember to carefully handle negative exponents and simplify the expression whenever possible.