Basic Math Exponents

Welcome back to Educator.com; this lesson is on the introduction of exponents.0000

When you have a number with an exponent, that number, this number right here, 10, is called the base.0010

This 2 is called the exponent.0019

This can be read as 10 squared, or 10 to the power of 2, or 10 to the 2nd power.0025

Whenever you have a base with a number that is a little bit higher to the side of it,0035

then that is called the exponent; you read it 10 to the power of 2.0041

Or if it is a 2, then you can just say 10 squared.0046

Find the value of 6 to the 3rd power.0054

Exponent, what that means is you are saying that 6 is going to be a factor 3 times.0059

When we have 6 to the 3rd power, we are going to write this out as 6 times 6 times 6.0070

It is just this number multiplied by itself that many times.0078

Be careful; this is not 6 times 3; this is not 18.0084

We have to write this out as 6 times 6 times 6; then you just solve this out.0088

We have 6 times 6 is 36; we have to multiply that by 6 again.0094

If you do 36 times 6, then you are going to get 6 times 6, 36.0101

This is 18; plus the 3 is 21; 6 to the 3rd power is 216.0107

Another example, this is written out in expanded form.0118

It is 4 times 4 times 4 times 4 times 4.0125

When we write that in exponent form, we are going to write the 4 as a base0129

because all these numbers are 4s so the base is going to be a 4.0135

How many times did it multiply by itself?0140

1, 2, 3, 4, 5; there is 5 of them.0143

I am going to write that as my exponent.0146

It is going to be 4 to the 5th power.0148

4 to the power of 5 or 4 to the 5th power.0152

Write 125 using an exponent and the base 5.0159

That means we want the base to be a 5.0163

We are going to have to see what the exponent is going to be0167

so that when we solve that out, it is going to become 125.0170

Base is 5.0176

Again I need to find a number that goes there as my exponent0178

so that when I solve this out, it is going to become 125.0183

First, in order for me to do this, I have to see0188

how many times I have to multiply 5 to itself to get 125.0191

125 is going to be... this is called the factor tree.0198

We haven't gone over that yet; it is later on in the lesson.0203

But we are just going to break this up; 125 is 25 times 5.0208

25 times 5 is 125; this 25 is 5 times 5.0216

That means 5 times 5 times this 5 gives you 125.0223

This can be written out as 5 times 5 times 5.0234

5 times 5 is 25; 25 times 5 is 125.0240

To write this using base 5, my exponent is going to be... how many times did I multiply 5 to itself?0246

3 times; it is going to be 3.0253

My answer is 5 to the 3rd power.0258

The next example, write the equal factors and the value of 3 to the 4th power.0268

The equal factors just means for you to write it out in expanded form.0274

It is 3 times 3 times 3 times 3.0281

Again, whenever you are solving exponents, make sure you write it out like this so you don't multiply 3 times 4.0286

This is not 12; be careful with that.0294

Exponents tell you how many times you are going to multiply this base number to itself.0296

We are going to multiply 3 to itself 4 times.0303

It is 3 times 3 times 3 times 3.0307

When I multiply this out, I can multiply these two first.0311

This is going to be 9; we can multiply these two; that is 9.0313

9 times 9 is 81; 3 to the 4th power is 81.0318

That is it for this lesson on exponents; thank you for watching Educator.com.0329