Solving Exponential Expressions
In this article, we will solve an exponential expression problem that involves multiplying two exponential terms. The problem is: 2.5 x 10^3 times what number is equal to 5 x 10^6.
Understanding Exponential Notation
Before we dive into the solution, let's quickly review exponential notation. Exponential notation is a shorthand way of writing repeated multiplication of a number by itself. For example, 10^3 means 10 multiplied by itself three times, or 10 × 10 × 10.
Setting Up the Equation
Let's set up the equation based on the problem:
2.5 x 10^3 × x = 5 x 10^6
where x is the unknown number we are trying to find.
Simplifying the Equation
To simplify the equation, we can start by rewriting the exponential terms using the rule of exponents that states a^m × a^n = a^(m+n).
2.5 × 10^3 × x = 5 × 10^6
Since the base of the exponential terms is the same (10), we can rewrite the equation as:
2.5 × x = 5 × 10^(6-3)
2.5 × x = 5 × 10^3
Solving for x
Now, we can solve for x by dividing both sides of the equation by 2.5.
x = 5 × 10^3 / 2.5
x = 2 × 10^3
x = 2000
Answer
Therefore, 2.5 x 10^3 times 2000 is equal to 5 x 10^6.
