Properties of Exponents Mr Preiss Algebra 2 Relax

Properties of Exponents Mr. Preiss Algebra 2

Relax, you aren’t in any trouble. This exponent stuff is a piece of cake. In this activity you will be maneuvering your way through every exponent property. In order to advance through the lesson, you must select the right responses and move ahead to the next property. If you make a mistake, you will be guided back to the property to try again. Upon completing every lesson, you will be required to take a 10 question quiz. Be sure of your answers though, one slip and you are sent back to the properties and have to start all over!

The Properties Product of Powers Power of a Product Zero Exponent Power of a Power Quotient of Powers Negative Exponents Power of a Quotient The Quiz

Product of Powers �When multiplying like bases, we have to ADD their exponents xm • xn = xm+n Example: x 3 • x 4 = x 7 Now you choose the correct answer… x 5 • x 6 = ? x 30 x 56 x 11

Sorry! Try Again! Remember, if you are multiplying like bases, we do NOT multiply the exponents

Notice if we were to break up the previous problem as the following… x 5 • x 6 = ? x • x • x • x Since x 5 means x times itself five times and x 6 means x times itself six times. How many of the x times itself did we end up with?

Return to The Properties

Notice if we were to break up the previous problem as the following… x 5 • x 6 = ? x • x • x • x Since x 5 means x times itself five times and x 6 means x times itself six times. How many of the x times itself did we end up with?

Power of a Power �When a base with a power is raised to another power, we MULTIPLY their exponents (xm)n = xm • n Example: (x 2)8 = x 16 Now you choose the correct answer… (x 3)4 = ? x 12 x 34 x 7

Sorry! Try Again! Remember, if you have a power to a power, we do NOT add the exponents

Now if we were to break up the previous problem as the following… (x 3)4 = ? (x • x)4 And continued to break these up using the ideas from the first property, we could get… (x • x • x) • (x • x) How many of the x times itself did we end up with?

Return to The Properties

Now if we were to break up the previous problem as the following… (x 3)4 = ? (x • x)4 And continued to break these up using the ideas from the first property, we could get… (x • x • x) • (x • x) How many of the x times itself did we end up with?

Power of a Product �When a product is raised to a power, EVERYTHING in the product receives that power (xy)m = xm • ym Example: (xy)7 = x 7 • y 7 Now you choose the correct answer… (xy)2 = ? x 2 y 2 xy 2

Sorry! Try Again! Remember, if you have a product to a power, ALL terms must receive that power

Now if we were to break up the previous problem as the following… (xy)2 = ? (xy) • (xy) And thinking about what happens when we multiply like bases, what would the powers of each variable be?

Return to The Properties

Now if we were to break up the previous problem as the following… (xy)2 = ? (xy) • (xy) And thinking about what happens when we multiply like bases, what would the powers of each variable be?

Quotient of Powers �When dividing like bases, we have to SUBTRACT their exponents = xm-n Example: = x 6 Now you choose the correct answer… =? x 8 x 24

Sorry! Try Again! Remember, if you are dividing like bases, do NOT divide their exponents

Now if we were to break up the previous problem as the following… Looking at the x’s in the numerator and the denominator. If every x in the numerator was cancelled by one in the denominator, how many of the x times themselves would be left and where would they be?

Return to The Properties

Now if we were to break up the previous problem as the following… Looking at the x’s in the numerator and the denominator. If every x in the numerator was cancelled by one in the denominator, how many of the x times themselves would be left and where would they be?

Power of a Quotient �When a quotient is raised to a power, EVERYTHING in the quotient gets that power = Example: = Now you choose the correct answer… =?

Sorry! Try Again! Remember, if you have a quotient to a power, ALL terms receive that power

Now if we were to break up the previous problem as the following… Looking at the x’s being multiplied in the numerator and the y’s being multiplied in the denominator, how many of the x times themselves are in the numerator and how many of the y times themselves are in the denominator?

Return to The Properties

Now if we were to break up the previous problem as the following… Looking at the x’s being multiplied in the numerator and the y’s being multiplied in the denominator, how many of the x times themselves are in the numerator and how many of the y times themselves are in the denominator?

Zero Exponent �Anything to the power of zero is ALWAYS equal to one x 0 = 1 Example: (4 xy)0 = 1 Now you choose the correct answer… (9 x 5 yz 17)0 = ? 1 0 x

Sorry! Try Again! Remember, if anything has zero as an exponent, that does NOT mean it equals zero Return to last slide

Return to The Properties

But Why? For a brief look at why anything to the power of zero is one, take a look at a few explanations here.

Negative Exponents �We can never have a negative exponent, so if we have one we have to MOVE the base to make it positive. If it is on top it goes to the bottom, if it is on bottom it goes to the top. x-m = or = xm Example: = x 4 Now you choose the correct answer… x-3 -x 3

Sorry! Try Again! Make sure to move the variable and make the exponent POSITIVE Return to last slide

Return to The Properties Take The Quiz

Simplify the following quiz questions using the properties of exponents that you have learned in the activity. Question #1: y 4 • y 5 = ? y 20 y 9 y 45