Assignments: 02-Exponents
When dealing with exponents there are two specific numbers we need to be aware of. Each exponent has a base number and the exponent. Let’s take the exponent 3⁵ (said ‘three to the fifth power’). The base number is the 3 and the exponent is the 5.
Now, exponents are considered to be repeated multiplication where you multiply the same number by itself.. The base number tells you which number to multiply, and the exponent tells you how many times to multiply it. so if we take the same 3⁵, it will be the 3 that we multiply by itself (3×3, etc.) The five tells us to multiply it 5 times. There are three different ways we can represent this.
Exponent Form: 3⁵
Product Form: 3 x 3 x 3 x 3 x 3
Standard Form: 243
There are also different ways we can say certain exponents. Specifically, a number to the second power (ex. 4²), which could be said four squared. The reasoning behind this comes later when we begin our geometry unit. To find the area of a square, you times the side by itself. The other exponent that has a special name is any number to the third power (ex. 4³), which would be said four cubed. Again, the basis for this comes from geometry. When we find the volume of a cube, we times the side by itself 3 times.
The final idea within this lesson is another form for writing numbers. It incorporates both expanded form and exponents. It is used a lot in science when we discuss distances in space that are far more miles than we’d want to completely write out every time. I will use a smaller number for an example:
Let’s take the number 4,512. Broken into expanded form it would be 4,000+500+10+2. We know that 4000 would be equal to 4 x 1,000, so we could break that entire number apart so it looks like the following:
(4 x 1,000) + (5 x 100) + (1 x 10) + (2)
Now, one thing we need to make clear is that any number to the zero power is one. So if I were ask you to evaluate 10⁰, it would equal 1. We also need to be familiar with our powers of 10. For this example, we only need up to 10³, but for even larger numbers the idea remains the same. 10³=10x10x10=1,000. 10²=10×10=100. 101 = 10. 100=1. With that in mind, our expanded number above could be written as follows:
(4 x 10³) + (3 x 10²) + (1 x 101) + (2 x 100)
You can see how this would come in handy when dealing with such numbers as given in the example for Place Value. Rather than having to write out all of those zeroes, you could simply write:
(5 x 1014) + (7 x 1013) + (7 x 1012) + (8 x 1010)