Question

which expression is equivalent to $5^{10}\bullet5^{5}$? $5^{2}$ $5^{5}$ $5^{15}$ $5^{50}$

Explanation:

Step1: Recall exponent rule for multiplication

When multiplying two exponents with the same base, we use the rule \( a^m \cdot a^n = a^{m + n} \). Here, the base \( a = 5 \), \( m = 10 \), and \( n = 5 \).

Step2: Apply the rule

Substitute the values into the rule: \( 5^{10} \cdot 5^{5} = 5^{10 + 5} \).

Step3: Calculate the exponent

Add the exponents: \( 10 + 5 = 15 \), so \( 5^{10} \cdot 5^{5} = 5^{15} \).

Answer:

\( 5^{15} \) (corresponding to the option with \( 5^{15} \))