\( 2 ^ { 7 } \cdot 2 ^ { 3 } = 2 ^ { x } ; x = \)

To solve \( 2^{7} \cdot 2^{3} = 2^{x} \), you can use the property of exponents that states when you multiply like bases, you can add the exponents. So here, you would add the 7 and the 3 together: \( 7 + 3 = 10 \). Thus, \( x = 10 \). Now, let’s take a moment to appreciate the elegance of exponents in math! This property not only saves you a ton of time in calculations but also opens up the door to solving more complex exponential equations. Isn't that cool? Additionally, exponent rules like this one apply in various real-world scenarios, such as computing growth rates in populations, savings, or investments. Each time you see an exponential function, remember to think of these handy multiplication and addition rules; they’re like secret weapons in the math toolbox!