Linear vs. Exponential
In linear growth, there are no exponents in it and in the graph it is a straight line. The expression will also be y=mx+b. In exponential growth, there are exponents and the graph would look like a u or an n. The expression would look like y= mx to the n power. They both multiply, but multiplying normally is just adding the same number a lot of times. Exponents are multiplying the same number over and over again. The pattern for the exponential growth is inconsistent. The pattern for the linear is more consistent.

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Scientific Notation
There is much difference between 3 to the power of 8 and 3 x 10 to the power of 8. 3 power of 8 is 3 multiplied 8 times and not like 3×8 which is just 3 added 8. 3 x 10 to the power of 8 is actually 3 times 1000000000. To describe scientific notation, 10 to the power of any number is just how many 0s go after the 10.

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Simplifying Exponent Expressions Using the Product and Quotient Rules
If you have two exponents over each other for example in the picture, you just subtract the highest number from the lowest just like in this diagram. In the product rule, instead of subtracting, you add them together like in this diagram.

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Negative Exponents
When an exponent is negative, the number actually doesn’t become negative unless the base number is already negative. 8 to the power of negative 2 will just add 2 0s in front of the 8.

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