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Power of Powers: Simplifying Exponential Expressions

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  • 0:07 Math Building Blocks
  • 0:42 The Base of an…
  • 0:54 The Exponent
  • 1:13 Raising a Power to a Power
  • 3:08 Lesson Summary
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Lesson Transcript
Instructor: Jennifer Beddoe
Mathematics is a very logical science. There is a rule for everything and not many exceptions to those rules. Working with exponents is no different. This lesson will describe the rule for raising a power to a power and also will give some examples in how to solve them.

Math Building Blocks

I love Legos. There are so many options! Different colors, sizes, shapes, kits - the possibilities are endless. One day you can build a town, the next day a scene from a movie and the next day you can decide to just pile all the blocks into one free-form structure with no real purpose.

Even though there might not be as much creativity in mathematics as there is in playing with Legos, we end up doing a different kind of building when dealing with numbers and variables. And exponents even have that look of building and expanding. They always remind me of working with blocks.

The Base of an Exponential Term

The ground floor of any exponential term is called the base.

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In this term, the base is the number 2.

The ground floor of an exponent can be any number or variable.

The Exponent

The next floor of an exponential term is the exponent - the 3 in this case.

The exponent tells you how many times to multiply a number to itself.

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Raising a Power to a Power

As with Legos, there are times when the exponential term has a third floor. This is called raising a power to a power and looks like this:

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These exponential terms can be simplified by writing them out like this, which can then be written as:

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which simplifies to 5^6 because there are six 5s being multiplied together.

If we look back to the original problem, we see that by multiplying the two exponents together, we also get 6.

2*3 = 6

So we can assume from this that to simplify a term with a power raised to a power, you just need to multiply the exponents together. But let's try another example.

Simplify:

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Simplifying the long way gives us:

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which equals a whole bunch of xs. When you add them up, you see it's x^15.

If we multiply the exponents we get:

3*5 = 15

so

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Again we see that the exponents can be simplified by multiplying the two exponents together.

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