Understanding How to Solve Complex Exponential Expressions Like a Pro

The result of (250 x 10^-6) - (7 x 10^-5) is?

• A. 170 x 10^-6
• B. 180 x 10^-6
• C. 190 x 10^-6
• D. 200 x 10^-6

Answer: (B)

To solve the expression (250 x 10^-6) - (7 x 10^-5), it's important to express both terms with the same exponent for the base of 10. Start by adjusting the second term, 7 x 10^-5, to match the exponent of the first term, which is -6. This can be accomplished by converting 7 x 10^-5 to a form with a power of 10^-6: 7 x 10^-5 = 7 x 10^-5 x (10^1 / 10^1) = 70 x 10^-6. Now the expression looks like this: (250 x 10^-6) - (70 x 10^-6). Next, combine the coefficients while maintaining the same power of 10. You subtract 70 from 250: 250 - 70 = 180. Therefore, the result is: 180 x 10^-6. This confirms that the correct answer is indeed 180 x 10^-6, which directly corresponds with one of the options provided. It's also crucial to perform the operation in the correct order and ensure that both terms are aligned in terms of their exponential notations for an accurate result.

What’s the Big Deal About Exponential Expressions?

When it comes to math, exponential expressions can feel a little intimidating at first. But let’s be real—you’re here to summon your inner math wizard, and that’s a fantastic goal!

In the world of technical skills and installation technician expertise, knowing how to handle math like this is crucial. Whether you’re balancing wiring diagrams, calculating signal losses, or adjusting voltage, the fundamentals of exponential math provide a solid backbone to your toolkit.

Breaking Down the Problem

So, let’s tackle a specific question that you might encounter in your learning journey. Suppose you’re tasked with figuring out the result of this expression:

(250 x 10^-6) - (7 x 10^-5)

Looks a bit daunting, huh? Don’t worry; we’ll break it down together!

Step 1: Aligning Exponents

The trick here is to get both terms aligned with the same exponent base. Right now, we’ve got:

• Term 1: 250 x 10^-6

• Term 2: 7 x 10^-5

To work with these effectively, we need to adjust the second term to match the first. So, let’s convert the 7 x 10^-5 into something more manageable.

Here’s how we do it:

7 x 10^-5 = 7 x 10^-5 * (10^1 / 10^1) = 70 x 10^-6

Step 2: Bringing It All Together

Now we rewrite the original problem using our new term:

(250 x 10^-6) - (70 x 10^-6)

Easy-peasy, right? Now, with both terms in sync, we can combine them.

a) Just subtract the coefficients while keeping that power of ten consistent!

b) You know it:

250 - 70 = 180

The Final Result

Bingo! You’ve done it! The end game results in:

180 x 10^-6

Seems simple enough, right? And, double-checking our options, this matches one of the given answers perfectly. Understanding how to navigate through these steps assures that you’re on the right track.

Real-World Connections

Now, why does this matter? Well, in technical jobs, having strong math skills goes beyond just passing tests. It’s about applying these concepts to real-world situations. Whether you’re configuring installations or analyzing electrical loads, being comfortable with numbers will give you confidence in making those critical decisions.

Being able to break down complex problems like this one demonstrates not just knowledge, but also practical skills in communication—those conversations with your colleagues about project specifics will flow much more smoothly.

So next time you face another challenging expression, remember the steps we covered. You’ve got the skills to sort it out. Keep pushing your boundaries and embrace the learning process—who knows what you’ll tackle next?