Raising and lowering indices

When we talk about indices in math, we're talking about the little numbers that sit up high and tell us how many times we have to multiply a number by itself.

But sometimes those little numbers need to move up or down to make things simpler. When we "raise" an index, we move it up higher by one spot. This means we need to divide the number by itself.

For example, let's look at the number 2 to the 3rd power: 2^3. This means we multiply 2 by itself 3 times, so we get 2 x 2 x 2 = 8.

But what if we want to "raise the index" to 4? Then we take that 8, and divide it by 2. So we get 8/2 = 4, and write it as 2^4 instead.

On the other hand, when we "lower" an index, we move it down lower by one spot. This means we need to multiply the number by itself.

For example, let's look at the number 5 squared: 5^2. This means we multiply 5 by itself 2 times, so we get 5 x 5 = 25.

But what if we want to "lower the index" to 1? Then we take that 25, and multiply it by 5. So we get 25 x 5 = 125, and write it as 5^1.

So that's how we raise and lower indices! It's all about moving those little numbers up or down to make things simpler.