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Hello, everyone.

This lesson is on higher powers.

Here is three squared.

There's other ways of saying this expression, we can call this number, the base number.

We can call this number, the power or the index.

Some people even call it the exponent.

How do we calculate this? Well, three squared or three to the power of two is equal to three times by three.

Now let's look at higher powers.

In this example, we have three raised to the power of four.

Here's the base number, here's the power or the index.

How do we calculate it? Well, three raised to the powerful is equal to three times by three times by three times by three.

Here is a sequence.

The numbers all have a base of two and a raised by consecutive powers.

For example, two to the power of one, two to the power of two, two to three, et cetera.

Anything raised to the power of one is just the base number.

Two squared equals two times by two, which is four.

Two cubed equals eight, two to the power of four is 16.

Watch how this sequence develops.

Here is a different sequence, here, these numbers have a base of negative two and are raised by consecutive powers again.

Watch how this sequence develops.

So what did you notice about these two sequences? Do you see some of results are the same? Whenever we have even powers, no matter whether the base number is positive or negative, we end up with positive answers.

Whenever we have odd powers, with negative basis, we end up with negative answers.

So here are some questions for you to try.

Once you've finished, pause the video and come back and check your answers.

Here's the solutions to questions one and two.

What did you notice about question two? Did you notice that every time it was doubling, if you had a base number of three every time, if you were using consecutive powers, I, the power of two, the power of three, the power of four with a base of three, each answer would triple.

Here's some more questions for you to try pause the video and return or to look at your answers.

Here are the questions to three, four, and five.

In question five, you have to be able to use the skill of evaluating higher powers with base 10.

Also, it's a really good thing to be able to name those numbers.

For example, 10 to the power of six is one million.

Let's have a go at question six, pause the video and return when you want to check your answers.

Here's the solutions to question six.

Quite like question G, a half and 0.

5 are the same value raised to the power of five.

They will also be the same value.

Why might we use a fraction? Well, two to the power of five gives us an answer of 32.

So it's easy to see that this is one over 32 as a fraction.

Sometimes that's useful, especially in higher mathematics.

Final questions now, well done to get this far, really well done, keep it up.

And here are the final solutions.

It's nice to note that negative basis raised to even powers.

Always give you a positive result.