### The Question:

I received the following email from my Mom the other day. (She's been a middle school teacher since the early '90s). She wrote:

Jon, I received The Question today from one of my 7th graders today: "When am I ever going to need to know how to do this???" He is working on zero and negative exponents and had to solve problems like this:

Write an equivalent expression for

The answer was

He understands how to do the problems--just wants to knowwhyhe needs to know, why it'snota waste of his time.

### My Response:

Good questions! I wrote a blog post about the matter... let me know what you tell him. I'd love to hear how he responds.

http://profjonh.blogspot.com/

### That Blog Post (AKA, This Blog Post):

My colleague answers that question this way:

(Read his full blog post at: http://deltascape.blogspot.com/2012/05/when-will-we-ever-use-this.html)I don't know when or if you will ever need this particular concept. It depends on what you do with your life and what technological advances are made in the future. But you know what you will need to be able to do, regardless? You will need toproblem solve. You will need to think critically (reason and prove). You will need to be able tocommunicatequantitative thinking to others. You will need to userepresentationsto support your thinking and share your thinking. And you will need to makeconnectionsin order to consolidate your understanding. Mathematics is a discipline that provides opportunities to practice and strengthen all of these skills. So, as we solve forx, I want you to monitor your thinking because that's what's really important.

He's talking about the Process Standards from NCTM (2000), which are now reflected in CCSS Standards for Mathematical Practice:

But just in case that argument doesn't satisfy your young math skeptic, you might want to share the following list of websites with him (see below). It turns out rational exponents are at the heart of a great many useful scientific formulas, not to mention a lot of really cool (and really beautiful) mathematics!

Good luck!

- Jon

#### Seven applications of rational exponents:

- Chemistry:

http://chemwiki.ucdavis.edu/Physical_Chemistry/Kinetics/Rate_Laws/The_Rate_Law - Modern Physics (Albert Einstein):

http://en.wikipedia.org/wiki/Mass%E2%80%93energy_equivalence#Mass-velocity_relationship - Classical Physics (Isaac Newton, born on Christmas Day, 1642!):

http://www.logrog.net/users/lkovach/physics/Universal%20Gravitation/Days%201-3.pdf - Rocket Science:

http://exploration.grc.nasa.gov/education/rocket/isentrop.html - Astronomy:

http://scioly.org/wiki/images/c/c6/Formula_Sheet.pdf - Wall Street investment trading:

http://fr.accuracy.com/visuels/28t-1271338388.jpg - Renewable Energy (Wind):

http://www.raeng.org.uk/education/diploma/maths/pdf/exemplars_advanced/23_wind_turbine.pdf

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