it helps you solve and understand expression faster. it turns long problems it too short ones
Rules for exponents to multiply powers, add the exponents to divide powers, subtract the exponents to find a power of a power, multiply the exponents to find a power of a quotient, apply the power top and bottom to find a power pf a product, apply the exponent to each factor in the product x0 = 1 anything to the power zero equals one x-a = 1/xa a negative exponent means "one over" the positive exponent
A rational exponent is an exponent in the form of a fraction. Many financial formulas use rational exponents. Compound interest is formula that uses rational exponents.
bacterial growth for one. exponents are used in equations when representing things. growth is the main thing, growth of possibilities(ie. possible outcomes of a situation) another example of a growth calculation would be calculating interest on a loan or a credit card or a savings account (if its compound interest, which most is these days) if you want to get advance, the hardy weinberg equation is used for mapping the gene pool of a population, and it has exponents. also, wave functions of particles. also, it's how ARE exponents used in real live?
You multiply the exponents.
it helps you solve and understand expression faster. it turns long problems it too short ones
It is when you apply your data to the real world, and how it can help you in the real world.
In construction, if you wanted to paint a room or lay down carpet you need to know the area, which is done in square feet. This is a real world example that is useful, so that you don't over spend on useless supplies or get too few.
Adaptation
Rules for exponents to multiply powers, add the exponents to divide powers, subtract the exponents to find a power of a power, multiply the exponents to find a power of a quotient, apply the power top and bottom to find a power pf a product, apply the exponent to each factor in the product x0 = 1 anything to the power zero equals one x-a = 1/xa a negative exponent means "one over" the positive exponent
External Validity
A rational exponent is an exponent in the form of a fraction. Many financial formulas use rational exponents. Compound interest is formula that uses rational exponents.
Scientific notation is a way to write very large or very small numbers using exponents. For example 2000 is 2x103 . We can do the same thing with negative exponents and write very small numbers like 1/2000 which is 2x10-3 . So one real life use of exponents in in scientific notation.
No. The context need not be a real world setting. If I am writing a Science Fiction book, my contextual intelligence would be the ability to use and apply the knowledge that is appropriate to my fictional world. If I were any good as a writer, that would not be the real world setting but a convincing but unreal extension of it.
You could compare it to water distilling.
Yes, it does.
Exponents make the question shorter. Ex: 2.30134 x 106=2301340. Instead of saying 2.30134 x 10 x 10 x 10 x 10 x 10 x 10=2301340