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Algebra I: High School20 chapters | 168 lessons | 1 flashcard set

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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.

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 ground floor of any exponential term is called the base.

In this term, the base is the number 2.

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

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.

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:

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

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:

Simplifying the long way gives us:

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

If we multiply the exponents we get:

3*5 = 15

so

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

This rule also applies when there are negative exponents.

Simplify:

By simply multiplying the exponents together we see that the answer is:

(2)*(-4) = -8

so

Let's work it out the long way as proof.

As you can see when you count up all the *b*s, we get *b*^-8 as the answer, proving that the multiplication method works.

Exponents can build upon each other just like Lego blocks can build upon each other. When you are simplifying exponential terms raised to another exponent, the way to simplify them is to multiply the exponents together. This will work with positive and negative exponents and can be shown by working out each exponent the long way.

After watching this lesson, you should be able to interpret the rule for raising a power to a power and give examples to solve these expressions.

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Lesson
9 in chapter 5 of the course:

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Algebra I: High School20 chapters | 168 lessons | 1 flashcard set

- How to Use Exponential Notation 2:44
- Scientific Notation: Definition and Examples 6:49
- Simplifying and Solving Exponential Expressions 7:27
- Exponential Expressions & The Order of Operations 4:36
- Multiplying Exponential Expressions 4:07
- Dividing Exponential Expressions 4:43
- The Power of Zero: Simplifying Exponential Expressions 5:11
- Negative Exponents: Writing Powers of Fractions and Decimals 3:55
- Power of Powers: Simplifying Exponential Expressions 3:33
- Go to High School Algebra: Exponents and Exponential Expressions

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