Question

Which are the correct steps to follow to simplify an exponential expression using the Quotient Rule of Integer Exponents?(1 point)
Responses

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.
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.

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.

Answer 1

The correct choice is the third one:

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

Brief notes:
- Quotient rule: a^m / a^n = a^(m−n) for a ≠ 0.
- If the result has a negative exponent, rewrite as a reciprocal: a^(−k) = 1/a^k.
- If bases are different but can be rewritten to a common base (e.g., 4^3/2^2 = 2^6/2^2), convert and then apply the rule.

Examples:
- x^5 / x^2 = x^(5−2) = x^3
- 2^4 / 2^6 = 2^(4−6) = 2^(−2) = 1/2^2 = 1/4