use the product rule of exponents to simplify 5^10 . 5^5

Answer 1

To simplify \( 5^{10} \cdot 5^{5} \) using the product rule of exponents, you add the exponents when multiplying numbers with the same base. The product rule states that \( a^m \cdot a^n = a^{m+n} \).

In this case:

\[ 5^{10} \cdot 5^{5} = 5^{10 + 5} = 5^{15} \]

So, the simplified form is \( 5^{15} \).