Question

which expression is equivalent to $5^5 \cdot 5^7$?
$5^{35}$ $\frac{1}{5^{12}}$ $(5^6)^6$ $5^{12}$

Explanation:

Step1: Recall exponent rule

When multiplying exponents with the same base, we use the rule \(a^m \cdot a^n = a^{m + n}\). Here, the base \(a = 5\), \(m = 5\), and \(n = 7\).

Step2: Apply the rule

Calculate \(5 + 7 = 12\). So, \(5^5 \cdot 5^7 = 5^{5 + 7}=5^{12}\).

Answer:

\(5^{12}\) (the option with \(5^{12}\))