Question

which expression is equivalent to $p^{9} \times p^{-5}$? \bigcirc $p^{-4}$ \bigcirc $p^{45}$ \bigcirc $p^{14}$ \bigcirc $p^{4}$

Explanation:

Step1: Recall exponent rule for multiplication

When multiplying two exponents with the same base \( a^m \times a^n=a^{m + n} \), here base is \( p \), \( m = 9 \), \( n=- 5 \).

Step2: Apply the rule

\( p^{9}\times p^{-5}=p^{9+( - 5)}=p^{9 - 5}=p^{4} \)

Answer:

\( p^{4} \) (the option corresponding to \( p^{4} \))