which expression is equivalent to $5^{10}cdot5^{5}$?\n$5^{2}$\n$5^{5}$\n$5^{15}$\n$5^{50}$

Explanation:

Step1: Recall exponent - product rule

When multiplying two exponential expressions with the same base (a^m\cdot a^n=a^{m + n}), where (a = 5), (m = 10), and (n = 5).

Step2: Apply the rule

(5^{10}\cdot5^{5}=5^{10 + 5}).

Step3: Calculate the exponent

(10+5 = 15), so (5^{10}\cdot5^{5}=5^{15}).

Answer:

(5^{15}) (corresponding to the third option)