• – HERE ARE SOME MORE EXAMPLES OF USING THE DISTRIBUTIVE PROPERTY TO SIMPLIFY EXPRESSIONS. IN THE FIRST EXAMPLE WE HAVE -9P x THE QUANTITY P + 2. SO, WE WANT TO DISTRIBUTE -9P, WHICH MEANS WE WANT TO MULTIPLY -9P AND P AS WELL AS -9P AND 2. SO, WE’D HAVE -9P x P + -9 x 2. WELL, -9P x P IS GOING TO BE -9P TO THE SECOND OR -9P SQUARED, AND THEN WE’LL HAVE + (-18), BUT INSTEAD OF LEAVING IT IN THIS FORM AS + AND -, IT’S MORE COMMON TO WRITE THIS AS SUBTRACTING A POSITIVE. SO, THIS IS EQUIVALENT TO -9P SQUARED – (+18).…

• Hello. I’m Professor Von Schmohawk and welcome to Why U. In our last lecture we saw that addition and multiplication are both commutative operations. The order of numbers which are added or multiplied can be rearranged without affecting the result. As we saw, addition also has an “associative” property. According to the Associative Property of Addition three or more numbers which are added can be grouped in any way without affecting the result. Does this also apply to multiplication? Let’s start with our stack of 24 boxes and group them in different ways before multiplying. For instance if we group the two and the three we get four groups of…

• – WELCOME TO THE PRESENTATION ON THE PROPERTIES OF EXPONENTS. THE GOAL OF THIS VIDEO IS TO USE THE PROPERTIES OF EXPONENTS TO SIMPLIFY EXPRESSIONS. HERE IS A LIST OF THE PROPERTIES OF EXPONENTS WE WILL BE DISCUSSING TODAY. YOU MAY WANT TO PAUSE THE VIDEO NOW AND WRITE THESE DOWN. WE WILL CONSIDER THEM ONE AT A TIME. THE FIRST PROPERTY IS A PRODUCT PROPERTY. IT STATES IF YOU’RE MULTIPLYING AND THE BASES ARE THE SAME, YOU ADD THE EXPONENTS. LET’S TAKE A LOOK AT WHY THAT MAKES SENSE. IF WE WANT TO MULTIPLY 5 TO THE SECOND x 5 TO THE FOURTH, WE KNOW THAT 5 TO THE…

• – WELCOME TO OUR LESSON ON THE PROPERTIES OF LOGARITHMS. LET’S GO AHEAD AND GET STARTED. THE FIRST PROPERTY IS LOG BASE A OF 1 IS EQUAL TO ZERO AND THIS IS TRUE BECAUSE A TO THE POWER OF ZERO WILL ALWAYS EQUAL 1. AND IF WE WANT AN EXAMPLE OF THIS WE COULD SAY LOG 1 OF ANY BASE, LET’S JUST SAY 8, WILL ALWAYS EQUAL ZERO BECAUSE 8 TO THE ZERO IS EQUAL TO 1. PROPERTY 2 SAYS LOG BASE A OF A IS EQUAL TO 1 SINCE A TO THE POWER OF 1 WILL EQUAL A SO IF THE BASE AND THE NUMBER ARE THE SAME IT…

• – WE WANT TO USE THE DISTRIBUTIVE PROPERTY TO SIMPLIFY THE GIVEN EXPRESSIONS. SO, HERE WE HAVE 5 x THE QUANTITY X + 2. SO, WE NEED TO MULTIPLY THE 5 AND THE X AS WELL AS THE 5 AND THE 2, AND SOMETIMES YOU’LL HEAR DISTRIBUTION REFERRED TO AS MULTIPLICATION ACROSS ADDITION OR SUBTRACTION, AND THIS IS WHY. SO, WE’LL HAVE 5 x X + 5 x 2. WELL, 5 x X WOULD BE 5X, AND 5 x 2=10. SO, WE HAVE 5X + 10. IN THE SECOND EXAMPLE WE’RE DISTRIBUTING +3. SO WE’LL HAVE +3 x X – +3 x 9. SO WE’LL HAVE 3 x X –…

• Hello. I’m Professor Von Schmohawk and welcome to Why U. In our last lecture, we saw how the people on my primitive island of Cocoloco discovered addition and subtraction. Once we had invented addition and subtraction the Cocoloconians could calculate very complicated coconut transactions with great precision. But we soon found out that with only addition and subtraction some calculations could take a very long time. For instance, once a year, everyone on Cocoloco must donate three coconuts for the annual feast of Mombozo. So if all 87 inhabitants of Cocoloco each donate three coconuts then how many coconuts will we have for the feast? Before we discovered multiplication, we…

• We want to simplify the following expressions completely. The first expression is two x raised to the fourth power. Let’s first simplify this by expanding, and then we’ll simplify it again using the power property of exponents. Notice we have an exponent of four, which means we have four factors of the base, which is two x. So this is equal to two x, times two x, times two x, times two x. Once expanded, notice how we can see we have four factors of two and four factors of x, so we can write this as two to the fourth times x to the fourth, and we can evaluate…