Question

simplify the expression, if possible. (if the expression cannot be simplified, enter the given\frac{(k - 2)^{15}}{(k - 2)}

Explanation:

Step1: Recall exponent rule for division

When dividing two powers with the same base \( a \), we use the rule \( \frac{a^m}{a^n}=a^{m - n} \). Here, the base is \( (k - 2) \), \( m = 15 \), and \( n = 1 \) (since \( (k - 2)=(k - 2)^1 \)).
$$\frac{(k - 2)^{15}}{(k - 2)^1}=(k - 2)^{15-1}$$

Step2: Simplify the exponent

Subtract the exponents: \( 15-1 = 14 \). So the expression simplifies to \( (k - 2)^{14} \).

Answer:

\( (k - 2)^{14} \)