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Learn and Practice How to Use Exponents in a Word Problem

Are you familiar with exponents (powers)? Do you know for what and how they are used? Today, we are going to see an example that will help you to solve problems with exponents or powers.

If you need to review what powers are before learning how to use them in a word problem, you can check out our previous posts:

Exponents word problem


Lerna’s Hydra is a mythological character that appears in some stories such as the 12 Tasks of Hercules. The Hydra was a one-headed monster but when it is cut off, 2 more heads grow in its place. If a hero tried to conquer it by cutting off all of its heads every day, how many heads would the Hydra have on the third day? And at the end of 10 days of trying to kill it?

We are going to solve the first question in this problem by considering:

The first day, upon cutting the head off, the monster had two heads.

The second day, upon cutting both heads off, they doubled: 2 x 2 = 4 heads.

The third day, the heads doubled again: 2 x 2 x 2 = 8 heads

Finally, in order to know how many heads it had on the third day, we have multiplied by two, three times.

In order to solve the second problem, we had to do the same procedure but it’s a little larger scale.

In order to know how many heads the monster had in 10 days, we must do the following operation:

2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2

It is a lot, right? For this, it will be easier to write if we use exponents, expressing the same operation in the following style:


What do you think? It might not be actually easier to find the answer (without a calculator), but isn’t is neat to be able to use an exponent to write such a long multiplication problem in such a simple way?

We invite you to register in Smartick and try it for free if you want to continue learning math and how to solve problems.

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Diane Ackerman
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