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!
Product of Powers Power of a Power Power of a Product Quotient of Powers Zero Exponent Negative Exponents Power of a Quotient
Product of Powers When multiplying like bases, we have to ADD their exponents x m x n = x m+n Example: x 3 x 4 = x 7 Now you choose the correct answer… x 5 x 6 = ? x 30 x 56 x 11
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 x x x 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 x x x 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 (x m ) n = x m n Example: (x 2 ) 8 = x 16 Now you choose the correct answer… (x 3 ) 4 = ? x 12 x 34 x7x7
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 x) 4 And continued to break these up using the ideas from the first property, we could get… (x 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 x) 4 And continued to break these up using the ideas from the first property, we could get… (x 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 = x m y m Example: (xy) 7 = x 7 y 7 Now you choose the correct answer… (xy) 2 = ? x2yx2yx2y2x2y2 xy 2
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) 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) 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 = x m-n Example: = x 6 Now you choose the correct answer… = ? x8x8 x2x2 x 24
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… = ?
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: (4xy) 0 = 1 Now you choose the correct answer… (9x 5 yz 17 ) 0 = ? 1 0 x
Remember, if anything has zero as an exponent, that does NOT mean it equals zero Return to last slide
Return to The Properties
For a brief look at why anything to the power of zero is one, take a look at a few explanations here.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= x m Example: = x 4 Now you choose the correct answer… x -3 -x 3
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 y9y9 y 45
Time to head back and review the property Return to the property
Return to The Properties
Question #2: (d 6 ) 3 = ? d 63 d9d9 d 18
Time to head back and review the property Return to the property
Return to The Properties
Question #3: (ab) 5 = ? a5b5a5b5 ab 5 a5ba5b
Time to head back and review the property Return to the property
Return to The Properties
Question #4: = ? x2x2 x4x4 x 32
Time to head back and review the property Return to the property
Return to The Properties
Question #5: = ?
Time to head back and review the property Return to the property
Return to The Properties
Question #6: (97rst) 0 = ?
Time to head back and review the property Return to the property
Return to The Properties
Question #7: = ? a6a6 -a 6 a -6
Time to head back and review the property Return to the property
Return to The Properties
Question #8: (x 2 y 3 ) 4 = ? x6y7x6y7 xy 9 x 8 y 12
Be careful, you are using more than one property at a time here Return to the problem
Return to The Properties
Question #9: (x 4 y 5 ) 2 ∙ (x 3 y 2 ) 3 = ? x 17 y 16 x 72 y 60 x 36 y 42
Be careful, you are using more than one property at a time here Return to the problem
Return to The Properties
Question #10: = ?
Be careful, you are using more than one property at a time here Return to the problem
Congratulations! You really know your exponent properties! Show Mr. Preiss this screen so can award you full credit for completing this activity.