Question

which expression is equivalent to $5^{10}\cdot 5^{5}$?\
\bigcirc $6^{2}$\
\bigcirc $5^{5}$\
\bigcirc $5^{15}$\
\bigcirc $5^{50}$

Explanation:

Step1: Recall exponent rule for multiplication

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

Step2: Apply the exponent rule

Using the rule \(5^{10} \cdot 5^{5}=5^{10 + 5}\)

Step3: Calculate the sum of exponents

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

Answer:

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