Question

selected response: 1 point for correct answer only
simplify: (\frac{a^{7}}{a^{4}})
(a^{11})
(a^{3})
(1)
(a^{28})

Explanation:

Step1: Recall exponent rule for division

When dividing exponents with the same base, we use the rule $ \frac{a^m}{a^n} = a^{m - n} $, where \( a \) is the base and \( m, n \) are exponents. Here, the base \( a \) is the same, \( m = 7 \) and \( n = 4 \).

Step2: Apply the exponent rule

Substitute \( m = 7 \) and \( n = 4 \) into the rule: \( \frac{a^7}{a^4}=a^{7 - 4} \)

Step3: Calculate the exponent

Simplify \( 7 - 4 = 3 \), so \( a^{7 - 4}=a^3 \)

Answer:

\( a^3 \) (corresponding to the option "a³")