unit 3: exponents, radicals, and exponential equations final exam review

UNIT 3: EXPONENTS, RADICALS, AND

EXPONENTIAL EQUATIONS

Final Exam Review

TOPICS TO COVERExponent RulesConverting Radicals to Fractional ExponentsConverting Fractional Exponents to RadicalsExponential Growth and DecayWord Problems

EXPONENT RULESMathematical Expressions can be simplified used exponent rulesHere are all of the rules:ADDING AND SUBTRACTING EXPRESSIONSMULTIPLYING EXPRESSIONSRAISING A POWER TO A POWERDIVIDING EXPRESSIONSNEGATIVE EXPONENTSZERO EXPONENTS

ADDING AND SUBTRACTING EXPRESSIONSWhen you are adding and subtracting exponents, you must:COMBINE LIKE TERMS only!Make sure to DISTRIBUTE the NEGATIVE when subtracting

Example:(4x2 + 9x – 6) + (7x2 – 2x – 1) = 11x2 + 7x – 7

(3x2 + 5x – 8) – (5x2 – 4x + 6) = -2x2 + 9x – 14

MULTIPLYING EXPRESSIONSWhen you are multiplying expressionsMULTIPLY the whole numbersADD the exponents

Example:(4x3)(2x2) = 8x5

(-4x5)(3x2) = -12x7

RAISING A POWER TO A POWERWhen you are raising a power to a power:RAISE the whole numbers to the powerMULTIPLY the exponents

Example:(5x2)4 = 625x8

(-3x6)3 = -27x18

DIVIDING EXPRESSIONSWhen you are dividing expressions:DIVIDE the whole numbersSUBTRACT the exponents

Example: =

=

NEGATIVE EXPONENTSWhen you have a negative exponentMOVE the negative exponent “TO THE OTHER BUNK”, meaning, move it to the other side of the FRACTION

When you move it, change the exponent to a POSITIVE because not it’s “HAPPY”

Example: =

= =

ZERO EXPONENTSWhen you have a zero exponentThe answer is always ZERO

Example: (5x4y2)0 = 1

= 1

PRACTICE ALL EXPONENT RULES1. (5x2 – 5x + 2) + (6x2 + 2x – 10) 2. (3x2 + 6x – 4) – (6x2 – 2x + 9)3. (6x4)(5x2)4. (4x2)3

5. (3x2y)0

CONVERTING A RADICAL INTO A FRACTIONAL EXPONENTParts of a radicalWhen converting a radical to a fractional exponent:The power inside the radical becomes the NUMERATORThe number in the INDEX becomes the DENOMINATOR

Example:

CONVERTING A RADICAL INTO A FRACTIONAL EXPONENTNow try these:

CONVERTING A FRACTIONAL EXPONENT INTO A RADICALWhen converting a fractional exponent into a radical:The numerator becomes the power INSIDE the radical

The denominator becomes the number in the INDEX

Example:

CONVERTING A FRACTIONAL EXPONENT INTO A RADICALNow try these:

EXPONENTIAL GROWTH AND DECAYExponential Functions can either represent GROWTH or DECAYEvery function follows this formula:y = a bx

a is the INITIAL valueb is the GROWTH or DECAY rateIf the problem is growth, use (1 + rate) for bIf the problem is decay, use (1 – rate) for b

x is the TIME

EXPONENTIAL GROWTH AND DECAYExampleWrite the equation for this situation:The amount of movies made in 2015 was 1,255. The number is expected to increase by 2.1% every year.

Answer: y = 1255(1 + 0.021)x

EXPONENTIAL GROWTH AND DECAYNow thy theseWrite an equation for these situations:1. The population of an ant colony with 5,056

members increases by 5.6% every year.2. The number of people who live in North

Dakota (who currently has 739,482 people) decreases every year by 1.3%.

WORD PROBLEMSThere are many real life situations that use exponential growth and decay. You can use these equations in order to predict outcomes in the future.In order to do this, use your calculator to put in the equation and use the table to find values.

WORD PROBLEMSTry this one:

The model y = 604000(1 + 0.045)x represent the population of Washington DC after 1990.1. Find the initial population2. Is this a growth or decay problem?3. Predict the population in 1995.4. In what year will the population reach 1,000,000?

ALL DONE