Which are the correct steps to follow to simplify an exponential expression using the Quotient Rule of Integer Exponents?

Question

Check if the bases are different; if they are, subtract the exponents of the numerator and denominator; and write the resulting expression in exponential form.
Check if the bases are different; if they are, subtract the exponents of the numerator and denominator; and write the resulting expression in exponential form.

Check if the bases are the same; if they are, subtract the exponents of the numerator and denominator (leave as-is otherwise); and write the resulting expression in exponential form.
Check if the bases are the same; if they are, subtract the exponents of the numerator and denominator (leave as-is otherwise); and write the resulting expression in exponential form.

Subtract the exponents of the numerator and denominator; and write the resulting expression in exponential form.
Subtract the exponents of the numerator and denominator; and write the resulting expression in exponential form.

Check if the bases are the same; if they are, add the exponents of the numerator and denominator (leave as-is otherwise); and write the resulting expression in exponential form.

Answer 1

To simplify an exponential expression using the Quotient Rule of Integer Exponents, you should follow these steps:

1. Check if the bases are the same. The Quotient Rule applies when you are dividing two exponents with the same base.
2. If the bases are the same, subtract the exponents of the numerator and the denominator. This is expressed mathematically as: \[ \frac{a^m}{a^n} = a^{m-n} \] where \(a\) is the base, \(m\) is the exponent in the numerator, and \(n\) is the exponent in the denominator.
3. Write the resulting expression in exponential form.

So, the correct option is:

Check if the bases are the same; if they are, subtract the exponents of the numerator and denominator (leave as-is otherwise); and write the resulting expression in exponential form.