Solving the Equation: 128√e^980
In this article, we will tackle a challenging equation that involves the exponential function and square roots. The equation is:
128√e^980
To solve this equation, we need to understand the properties of exponential functions and how to manipulate them.
Step 1: Simplify the Equation
The first step is to simplify the equation by evaluating the exponentiation. Recall that e^x is the exponential function, where e is a mathematical constant approximately equal to 2.718.
e^980 is an extremely large number, but we don't need to calculate its exact value at this point. We can simplify the equation by rewriting it as:
128√(e^980)
Step 2: Break Down the Square Root
Next, we need to break down the square root into its components. Recall that √x = x^(1/2), where x is a positive real number.
Applying this property to our equation, we get:
128(e^980)^(1/2)
Step 3: Apply the Exponent Rule
Now, we can apply the exponent rule, which states that (a^b)^c = a^(bc). In this case, a = e^980, b = 1/2, and c = 1/2.
(e^980)^(1/2) = e^(980/2) = e^490
Step 4: Simplify the Final Answer
Finally, we can simplify the final answer by combining the constant factor and the exponential function:
128(e^490)
And that's the solution to the equation 128√e^980! Note that the exact value of e^490 is an extremely large number, but we can leave it in this exponential form for simplicity.
Conclusion
In this article, we walked through the steps to solve the equation 128√e^980. By applying the properties of exponential functions and square roots, we were able to simplify the equation and arrive at a feasible solution.
