Linear vs. Exponential Growth
There is a difference between linear and exponential. This difference is fairly obvious because linear follows in a strict pattern and grows at a constant rate. The difference is most apparent when graphing because linear goes in a straight line and has the equation y=mx+b. On the other hand exponential equations are graphed with a curve and do not grow in a constant rate and has the equation y=ab^x.
Scientific Notation
Scientific notation is a way for people to write extremely large or small numbers using a number between 1 and 10 and an exponent. By using scientific notation we can use a completely different number while still keeping the same value for example: the number 500000000 can be rewritten as 5×10^8.
Simplifying Exponent Expressions Using The Product and Quotient Rules
A lot of exponent questions can be hard to understand but if you take certain steps you can make them a lot simpler and easier to solve. For example if you have the problem (6/8)^4 you can increase the numerator and denominator to the power. Using my example you take the numerator and raise it by the power of 4 and same with the denominator 6^4/8^4. Another problem such as 2^4/2^6 you subtract the exponents and keep the same bases.
Negative Exponents
There are also negative exponents. Whenever there is a negative exponent as it has the opposite effect and makes the number smaller. Negative exponents tell you basically how many times to divide the number by. For example 5^-2 would be 1/25 because it is a reciprocal of 5 and in scientific notation 5×10^-4 would be 0.0005.
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