**Video Transcript**

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Transcript
**Exponents and Division – the Quotient of Powers Property**

In the year 8008, data is the new money. The more you have, the more you control. We’re at the Schmoogle Headquarters at the lead data trader’s desk, model number AA-RN0, but everyone calls him Arn0. He seems really busy at his job as a data trader. Let’s take a closer look at what he’s working on.
He's talking to his head of engineering, Smicha, who needs to calculate the number of hard drives he needs in order to store all the data on the internet. AA-RN0 is making plans to backup the entire Internet, which is 10²⁵ brontobytes, to become the richest robot in the universe.

But Smicha only has 10¹⁵ brontobytes of space on each of his hard drives.
AA-RN0 has a problem. His **calculator** doesn’t show enough **digits** for an accurate **calculation**. Not knowing what to do, AA-RN0 asks Smicha if he has any ideas. Smicha knows a **method** to deal with **really large numbers** and thinks that his knowledge of **dividing exponents** might come in handy.

### Division of Exponents

Smicha shows AA-RN0 that **aᵐ / aⁿ = a⁽ᵐ⁻ⁿ⁾**, but he warns AA-RN0 that the **bases** of both numbers have to be the same. Smicha shows AA-RN0 a quick **example** with numbers instead of letters to help him understand **Exponents and Division**.

2⁵ / 2³ = 2⁽⁵⁻³⁾ = 2². As you know, this is the same as 32 / 8, which is 4, the same answer we just got. AA-RN0 gives the calculation another try. If the internet has 10²⁵ brontobytes of space, and each of their Gen1 hard drives can hold 10¹⁵ brontobytes of space, AA-RN0 notices that his **base** is 10, so he writes that down. He then writes 10²⁵ / 10¹⁵ and knows that this equals 10⁽²⁵⁻¹⁵⁾ which is the same as 10¹⁰. Smicha tells AA-RN0 that they need 10¹⁰ hard drives to store all the data.

*TEN BILLION ROBOTS!?!? THEY'LL NEVER FINISH!!!*

Good news! Smicha just received the Beta model for the Gen2 hard drive. The new Gen2 hard drives can each hold 10¹⁸ brontobytes of data. Smicha now needs to know how many Gen2 hard drives he’ll need to store all the internet’s data. He writes 10²⁵ / 10¹⁸. Following the steps Smicha outlined for him earlier, AA-RN0 rewrites the **division expression** as 10⁽²⁵⁻¹⁸⁾, which gives him 10⁷ hard drives. They only need to produce 10 million hard drives! They'll be done in a jiffy!

### Summary

In order to remember the steps for Exponents and Division, Smicha saves the equation in his memory. **aᵐ / aⁿ = a⁽ᵐ⁻ⁿ⁾**

When dividing exponents, if the bases are the same, you can simply subtract the exponents from the numerator and the denominator.

Smicha now has to make sure all the robots are built on time what’s this? I guess the future's not so different after all...

## 1 comment

Very cool! And informative!