Which is the value of this expression when a = negative 2 and b = negative 3?
(StartFraction 3 a Superscript negative 3 Baseline b squared Over 2 a Superscript negative 1 Baseline b Superscript 0 Baseline EndFraction) squared
StartFraction 4 Over 9 EndFraction
StartFraction 27 Over 8 EndFraction
StartFraction 243 Over 32 EndFraction
StartFraction 729 Over 64 EndFraction
Answers
Answer:
ExponentsOverviewRaising a base number x to the power of n => multiplying the base number x by itself n timesShorthand for multiplying the base number x by itself n times: x Superscript n question-mark Baseline equals yExponent (n) notation: x Superscript nOperationsProcedure to MULTIPLY numbers with exponents, given they have the same base => ADD the exponentsMultiplication example: x squared times x Superscript 5 Baseline equals x Superscript 2 plus 5 Baseline equals x Superscript 7Procedure to DIVIDE numbers with exponents, given they have the same base => SUBTRACT the exponentsDivision example: StartFraction x squared Over x cubed EndFraction equals x Superscript 2 minus 3 Baseline equals x Superscript negative 1ExamplesExponent example: 3 squared equals 3 times 3 equals 9Radicals / RootsOverviewOpposite of exponent - finding the base number x, given y (the result) and the exponent n of the base number - e.g. square root, cube rootTo find the base number x: x question-mark Superscript n Baseline equals yNotationsnth Root notation: RootIndex n StartRoot y EndRootSquare Root notation: StartRoot y EndRootCube Root notation: RootIndex 3 StartRoot y EndRootExamplesSquare Root example: x squared equals 9 x equals StartRoot 9 EndRoot equals 3LogarithmsOverviewThe exponent n for a given base number x and result yTo find the exponent n to determine how many times to multiply a base number by itself to get the given result: x Superscript n question-mark Baseline equals yLog notation: n equals log Subscript x Baseline left-parenthesis y right-parenthesisExamplesLog example: 5 Superscript n question-mark Baseline equals 25 n equals log Subscript 5 Baseline left-parenthesis 25 right-parenthesis n equals 2Common LogarithmThe "common logarithm" of a number is an exponential for the base 10"Common Log notation - default of base 10: log left-parenthesis y right-parenthesis equals log Subscript 10 Baseline left-parenthesis y right-parenthesisLog example: 10 Superscript n Baseline equals 1000 n equals log Subscript 10 Baseline left-parenthesis 1000 right-parenthesis equals log left-parenthesis 1000 right-parenthesis n equals 3Natural LogarithmThe "natural logarithm (ln)" of a number is an exponential for the base e, where e is a constant ~2.718Natural Log notation: ln left-parenthesis y right-parenthesis equals log left-parenthesis e right-parenthesisNatural Log example: log Subscript e Baseline left-parenthesis 64 right-parenthesis equals ln left-parenthesis 64 right-parenthesis equals 4.1589Inverse of Natural Log: e Superscript xDerivative of ln x: StartFraction 1 Over x EndFractionProperties / LawsDistributive PropertyAllows algebraic expressions in the form of a(b + c) to be reformulated to an equivalent expressionDistributive law: a left-parenthesis b plus c right-parenthesis equals a b plus a cKhan Academy: Distributive PropertyMonomialsMonomial - an algebric expression that contains only one termTrinomialsTrinomial - an algebric expression that contains only three termsFactoringRewriting a number or term as a product of several smaller factors or values in commonDifference of Squares PatternEvery polynomial that is a difference of square terms can be factored with this formula: a squared minus b squared equals left-parenthesis a plus b right-parenthesis left-parenthesis a minus b right-parenthesisKhan Academy: FactoringBinomialsOverviewBinomial - an algebric expression that contains only two termsOperationsDifference of Squares Pattern - special products of binomials (applying the Distributive Property twice): left-parenthesis a plus b right-parenthesis left-parenthesis a minus b right-parenthesis equals a left-parenthesis a plus b right-parenthesis minus b left-parenthesis a plus b right-parenthesis equals a squared plus a b minus a b minus b squared equals a squared minus b squared