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Exponents and Laws of Exponents

Added Aug 30, 2017 •

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Use this video to learn the laws of exponents and fill out the Laws of Exponents notes page.

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study off mr. coffee here coming to you from beautiful Atascocita Texas with another algebra lesson we're going to talk about exponents and the laws of exponents so get a piece of paper and a pencil and let's take some notes in this lesson you'll need to know your math facts you need to know how to add trakt multiply you need to know math vocabulary if you don't know what tell me a sore difference or product and excetera you need to get that down and you need to know your fractions very important skill in algebra is to who your fractions and in this lesson you will learn what is an exponent you'll learn how to use exponents and you will learn the laws of exponents  first what's an exponent and exponent shows how many times a number is a factor so look at our simple there we have x to the N power and what that tells us is the basis X  and the exponent is M we all refer to exponents as powers and noticed there that we have x x x x x into a half as many factors as there is an examples  x squared or x to the second power X Cube or x to the third power  and we have beaches power  combining exponents in order to add subtract you must have like terms which means you got to add apples apples and oranges to oranges X's go with x's these go with bees threes go with threes make some up so if you look at this example here we have x to the N plus x to the N plus x to the m we can only add the m gather and so we have two x to the N Power Plus x to the N power now for the law the exponents  the product of powers when multiplying with exponents add the exponents so we see we have x squared times x cubed 3 is 5 and so the answer x to the fifth power we add the exponents let's check out the proof x squared times x cube is X to the fifth power so will expand them and after expanding then we'll bring them together and no that's x to the fifth power just add the exponents I next part here is the power of a product apply the power to each factor and simplify so we have what three a b squared  which means then 3 squared a squared B squared and is 9 a squared B squared when we simplify pretty straightforward great tool to have and to Remember When dealing with higher orders later in Algebra 2  power of a power  when raising an exponent to a power how to play the Xbox x squared quantity to the 3rd power x squared times three H to the 6th power let's look at the proof of that  can't write out in expanded form can we go quotient of powers when dividing nexbox subtract the exponents X cubed divided by x squared  is the same as x to the Third X to witches x to the one which of course is X cuz we don't right ones least not when we're multiply  proof expand it up you got true well let's look here similar fraction love that cross him out and look what's left just one it's so it's true subtract the exponents Barber closure  find the power of the numerator and the denominator and simplify to a quantity to a be cute  Miss Keisha now we need to remember that the denominator cannot be zero and so 2 to the third power 8 of the third power + need to the third power the power of Plies to everything inside the parentheses and there we go simplified  radio 0 exponent this is very important rule anything raised to the zero power equals 1 anything raised to the zero R equals one keep that in mind very important skill and thing to remember later in a higher mathematics to the 0 equals 1 XY quantity x y - 0 equals 1 proof I love this proof whatever one is one X over X is 1  even a thousand over is what I think you get the idea executed executed one  and show X2 the 3-3 is X to the 0 therefore it must be one pretty easy using the rules of substitution  and reflexive anything to the zero power equals 1 negative exponents very important pitch into this Rule and negative power is a reciprocal 8 to the negative 2 is the same thing as one over a squared notice also the negative sign is not there anymore it's the negative exponent that means that this is a fraction of reciprocal  and 1/8 to the negative 2 tell us a reciprocal therefore equals a square and let's remember denominators can not be zero can't divide by zero people who's that last one  to look at there's a compound fraction and a fraction as a division problem so when you divide by a fraction can you flip the fraction and multiply and course as the fraction in the denominator  Wallace proof recap would you find exponents we stated the laws of exponents we learn how to use exponents and you should how tall you have any questions be sure to send an email to Mr class at mr. Causey. And I hope you have a great day

Uploaded by David Rowan.

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Exponents and Laws of Exponents

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