Find the quotient. \[ \frac{15^{8}}{15^{2}} \] A \( 15^{16} \) B \( \quad 15^{10} \) C \( \quad 15^{6} \) D \( \quad 15^{4} \)

To find the quotient \(\frac{15^{8}}{15^{2}}\), you can apply the laws of exponents, specifically the rule that states \(\frac{a^m}{a^n} = a^{m-n}\). Here, \(m\) is 8 and \(n\) is 2. So you subtract the exponents: \[ 15^{8-2} = 15^{6}. \] The correct answer is \(C \quad 15^{6}\). Now that you have the answer, wouldn't you like to know a bit about the historical significance behind exponents? Exponentiation dates back to ancient civilizations! The Egyptians used exponential growth concepts when calculating areas and volumes, while the Babylonians employed square and cube roots—an early nod to powers. It wasn't until the late 15th century that European mathematicians started formalizing the rules around exponents we use today. Thinking about real-world applications, exponents play a huge role in scientific notation, which simplifies the vast numbers we find in science (like the distance from Earth to stars!). When you're working on problems involving population growth or radioactive decay, you'll be applying those exponent rules without even realizing it—making math not just an academic exercise, but a real-world tool!