"Exponents become where I can just take the exponent out and bring it on to the front times the logarithm of the basic expression."
"Again, you can't leave exponents negative. Instead, you place them either in the denominator or numerator and with a positive exponent instead."
"Anything to the power of zero is equal to one."
"What makes a polom a polinomial is we have a variable or variables but namely we have to pay attention to the exponent on the uh those uh particular variables okay so what the exponent can be is basically a whole number zero and positive integers."
"So the basic gist of a negative exponent is that x to the power of negative one equals one over x."
"The first law says that if we have the base x with exponent m being multiplied by the same base x with exponent n, we can combine them simply by adding the exponents together."
"What do we have to multiply 2 to the 6 by to get back to the original 2 to the 8? This is really important."
"Just because it says 2 to the power of negative 1 does not mean the answer will be negative."
"That's how you simplify exponents that have additions or subtractions."
"Always remember: there are no rules for adding or subtracting exponents."
"When you see exponents with the same base an addition or subtraction, immediately think: what's the biggest thing I could factor out from everything?"
"When you have an exponent to an exponent, then you multiply those values."
"In order to get rid of a log, we need to raise both sides to the power of the base."
"If the bases are the same and you're multiplying, you just have to add the exponents up."
"When dividing with powers, subtract the powers."
"In algebra, when multiplying, we can add the powers."
"A continuing problem is always indices, making sure that you know your index laws."
"Any number to the power negative is the same as 1 over the number to the power positive."
"When you have x to the power half, this is the same as the square root of x."
"Any number to the power zero is one."
"If I want to come out from exponential to log, it's going to be log base two of eight is equal to three."
"When the bases are the same, you can start adding or subtracting exponents."
"The only way you can go as fast as possible is by understanding when you can add and subtract exponents."
"If you can solve the past five questions easily, there's nothing you really need to worry about, at least for exponents."
"Anything raised to the zero power is defined mathematically just to be the number one."
"You can add them, you can subtract them, you can multiply them."
"You add the exponents but you can't really add them because what's underneath the radical is different."
"Log base 3 of 9 is 2 because 3^2 is 9."
"These radicals... the square roots, the cube roots, the fourth roots, all of them really can be thought of and they really are equivalent to exponents, fractional exponents."
"Every one of these properties in this lesson really just come from the rules of exponents."
"When you realize that radicals are just exponents that are fractions, it becomes easy to understand where these come from."
"When you see a fractional exponent... the way you read it is, I have to take a cube root and I have to raise the thing to the fourth power, but the order actually doesn't matter."
"When we write an expression, we typically want any exponents first, if there are multiple exponents, write them from greatest to least."
"If you have a to the m times a to the n, you can simply add their exponents."
"To apply the laws of exponents, the bases must be the same."
"Out of a primitive root mod p, we can create a primitive root mod p to the k for any natural number k."
"A to the minus 1 plus 'b' to the minus 1 is not the same thing as 'a' plus 'b' to the minus 1."
"Always rewrite negative exponents immediately."
"The nth root of a to the M power will be written as a to the M over N."
"Immediately get away from the radical notation and get it into the exponential notation with rationals; it's much, much nicer."
"Always rewrite square root or the nth root of a as a to the 1 over N first, then proceed with whatever problem you're working on."
"What power do I need to raise 2 to, to get x?"
"Anything to the power of zero, except for zero to the power of zero, is equal to one."
"A power of a power means you keep the base and multiply the exponents."
"When dividing powers with the same base, you subtract the exponents."
"The negative exponent rule tells me it's equal to the reciprocal of the power with a positive exponent."
"If we've got b squared and all of that is being cubed, well that's just b squared times b squared times b squared which is going to be b to the power 6."
"3/4 to the power of negative 3 is going to be the same thing as 4/3 to the power of 3."
"Whenever you have a positive exponent, it's going to be a large number."
"Whenever you multiply two common bases, you can add the exponents."
"Anything to the power of zero is always one."
"Whenever we multiply two things with the same base we add their exponents."
"When we're dividing and we have our bases the same, we simply subtract our exponents."
"When you have an exponent raised to an exponent, those must be multiplied together."
"When you multiply and you have the same base, you actually add the exponents."
"When you are multiplying with the same base number, you can add the powers together."
"If you have exponents being multiplied together, this is the key thing for you: You add them together."
"The product property says if you have x to the m times x to the n, you have x to the m plus n."
"This base a can be any number greater than zero; we don't let it equal one."
"If you take this base a and raise it to that power y, you'll set it equal to x."
"If you have something raised to a power, this power can come out front as a factor."
"If you have an exponential a to the x and you put that inside of a logarithm, this is going to be equal to x."
"Any number in front of a logarithm is automatically an exponent."
"When the bases are the same, I simply bring down the base and add the exponents."
"Something special happens here, the reason why we're going to cross these out is because when you think about it, we are actually subtracting exponents."
"This is excellent since we're dividing common bases."
"This is one way that you can use fractional exponents to simplify roots."
"The product rule of exponents tells us that if we are multiplying variables that have the same base, we keep the base the same and we add the exponents."
"The quotient rule tells us if we are dividing powers that have the same base, we keep the base the same and we subtract the exponents."
"If we have fractional exponents, those represent roots for the bottom of the exponent and powers for the top of the exponent."
"If we have the same bases and we're multiplying, then we add our exponents."
"If a to the x equals a to the y, and our bases are the same, then your exponents also have to be equal."
"If 2 to the x equals 2 to the third, then x would equal 3."
"Anything to the power of one is equal to itself, anything to the power of zero is equal to one."
"When multiplying powers of 10, you add the exponents together."
"Remember, your variable remains wherever the largest exponent is."
"The power law of exponents tells me that if I have a power of a power, I can multiply the exponents together."
"When you have a bracket to a power like this, you can just multiply the powers."
"Laws of indices say we've got two numbers with the same base; we just simply add the indices."
"If we have x to the power of negative n, that's the same as 1 over x to the n."
"When you multiply them together, you add exponents."
"Multiplying like bases, you need to add the exponents."
"Working with radicals and working with powers and exponents, they basically go hand in hand."
"When you multiply two terms that have exponents together, then if the bases are the same, all you do is you add the exponents together."
"Simplifying expressions that involve exponents is just like we learned to simplify fractions, just like we learned how to simplify other things in math."
"All you got to do is take a whole number, raise it to the second power."
"When you divide, you just subtract the powers."
"The answer to the logarithmic expression is always an exponent."
"Any number to the power of zero is one, and any number to the power of one is always going to be itself."
"If you divide two terms of the same base, you subtract its powers."
"To undo the log, you use its inverse function, the exponent to the same base."
"0.2 cubed, we are saying we're going to do 0.2 multiplied by another 0.2 and multiply by another 0.2."
"If you have a negative power, all you do is you get the number to the power of one and put a one over it."
"If we add the exponents, that would be e to the 0 which is 1."
"When you're dividing powers with the same base, you subtract the powers."
"Anytime we have a fractional exponent, that represents a radical."
"Anything to the zero power, other than zero, is one."
"When you have a negative exponent, remember that base will be brought into the denominator."
"When we're dividing exponents, we subtract those exponents."
"Exponent rules: when I multiply common bases, I add those powers."
"If every term has reached a certain exponent n, then definitely we have a homogeneous differential equation."
"If we have an even power and an odd outside negative number, it becomes even."
"When we multiply two powers of the same base, we add the powers."
"When you want to solve an exponential, you use logarithms."
"When you raise an exponent to an exponent, you multiply the exponent."
"Positive integer exponents are simply a method of showing repeated multiplication by the same number."
"Any number to the zero is one, except for zero."
"Positive exponents mean to multiply, but negative exponents mean to divide."
"It's important that all of the major exponent properties are fluent within you, so that you can deal with them no matter what comes in terms of exponents."
"When you multiply two exponential expressions that have the same base, then their exponents will add."
"A fantastic property of exponents that always holds is that when we multiply the two together, as long as they've got the same base, then it just is that base raised to an exponent that is the sum of those two exponents."