Solve lambda^2-2/3+(2/3)^0+(-0.2)^2014*5^2014

$$\frac { \lambda ^ { 2 } - 2 } { 3 } + ( \frac { 2 } { 3 } ) ^ { 0 } + ( - 0.2 ) ^ { 2014 } \times 5 ^ { 2014 }$$

Evaluate

$$\frac{\lambda ^{2}+4}{3}$$

Short Solution Steps

Calculate \frac{2}{3} to the power of 0 and get 1.

$$\frac{\lambda ^{2}-2}{3}+1+\left(-0.2\right)^{2014}\times 5^{2014}$$

Calculate -0.2 to the power of 2014 and get 0.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001881097331137338612503073916809514162622165323102118216462569860015335442665259522222750902380963872634381868464517059008015759705478029855008245933943444578945105742156796395531284957564764895173491539805200158634501987756382426954912842154647000743459307463608932742085748811458532338066000514612761930651142863404801368155789385479092863941032915378183028780510521357607272581238559232684216613000269112917940574914593124841200091826747034554393245932485051874026372428326333186689598782787037275467864152892763767038416466516695974781074067878443132930874335703872681455957081545994439636601225697296384.

$$\frac{\lambda ^{2}-2}{3}+1+0.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001881097331137338612503073916809514162622165323102118216462569860015335442665259522222750902380963872634381868464517059008015759705478029855008245933943444578945105742156796395531284957564764895173491539805200158634501987756382426954912842154647000743459307463608932742085748811458532338066000514612761930651142863404801368155789385479092863941032915378183028780510521357607272581238559232684216613000269112917940574914593124841200091826747034554393245932485051874026372428326333186689598782787037275467864152892763767038416466516695974781074067878443132930874335703872681455957081545994439636601225697296384\times 5^{2014}$$

Calculate 5 to the power of 2014 and get 5316046030406016037338986508043745297765566249209831919338069598082451692752848763296349335204948657876931205552645947653933290021965537307789789321608298865418402491644468578154119338006536513579137306971418668939594138853253798470080974268441589799948909163522240889682672819871665399684954389561864086602240811872905979433694733133396588004689309488676997766179972885539951421080716595583973448099266911287641401434988273311261149091232066080543137174765018549767161084565470378898183375885357136003146833999904292115688921081458938810499867309342573618446468634735467519629330980230156985957944758525005577559493702993146807225361802167453489706384599072968062876158429907012794678374658052643106492832613851482088831697361117116847494275586263398055786306997629067970379802849648646327859385531315664221468756764866886951692283707932355333236655329299712264094434683517280694022189893587667362650855838281842572281093171232811366406220205355295423089611775315545429433386445430577991145354086222311974923494584494660778159201801527984393452312011041402180026454479649749840473191709867980992421153643751017781167243483858922176229514871642512868026698260541803296655591135248452444860843530452035448493044821843401743444654141348587919408512474301187596807969350497021662658923356898941281384404004041832682137331985942105359826170544941869730520779719379573257688476051185944015742279589176177978515625.

$$\frac{\lambda ^{2}-2}{3}+1+0.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001881097331137338612503073916809514162622165323102118216462569860015335442665259522222750902380963872634381868464517059008015759705478029855008245933943444578945105742156796395531284957564764895173491539805200158634501987756382426954912842154647000743459307463608932742085748811458532338066000514612761930651142863404801368155789385479092863941032915378183028780510521357607272581238559232684216613000269112917940574914593124841200091826747034554393245932485051874026372428326333186689598782787037275467864152892763767038416466516695974781074067878443132930874335703872681455957081545994439636601225697296384\times 5316046030406016037338986508043745297765566249209831919338069598082451692752848763296349335204948657876931205552645947653933290021965537307789789321608298865418402491644468578154119338006536513579137306971418668939594138853253798470080974268441589799948909163522240889682672819871665399684954389561864086602240811872905979433694733133396588004689309488676997766179972885539951421080716595583973448099266911287641401434988273311261149091232066080543137174765018549767161084565470378898183375885357136003146833999904292115688921081458938810499867309342573618446468634735467519629330980230156985957944758525005577559493702993146807225361802167453489706384599072968062876158429907012794678374658052643106492832613851482088831697361117116847494275586263398055786306997629067970379802849648646327859385531315664221468756764866886951692283707932355333236655329299712264094434683517280694022189893587667362650855838281842572281093171232811366406220205355295423089611775315545429433386445430577991145354086222311974923494584494660778159201801527984393452312011041402180026454479649749840473191709867980992421153643751017781167243483858922176229514871642512868026698260541803296655591135248452444860843530452035448493044821843401743444654141348587919408512474301187596807969350497021662658923356898941281384404004041832682137331985942105359826170544941869730520779719379573257688476051185944015742279589176177978515625$$

Multiply 0.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001881097331137338612503073916809514162622165323102118216462569860015335442665259522222750902380963872634381868464517059008015759705478029855008245933943444578945105742156796395531284957564764895173491539805200158634501987756382426954912842154647000743459307463608932742085748811458532338066000514612761930651142863404801368155789385479092863941032915378183028780510521357607272581238559232684216613000269112917940574914593124841200091826747034554393245932485051874026372428326333186689598782787037275467864152892763767038416466516695974781074067878443132930874335703872681455957081545994439636601225697296384 and 5316046030406016037338986508043745297765566249209831919338069598082451692752848763296349335204948657876931205552645947653933290021965537307789789321608298865418402491644468578154119338006536513579137306971418668939594138853253798470080974268441589799948909163522240889682672819871665399684954389561864086602240811872905979433694733133396588004689309488676997766179972885539951421080716595583973448099266911287641401434988273311261149091232066080543137174765018549767161084565470378898183375885357136003146833999904292115688921081458938810499867309342573618446468634735467519629330980230156985957944758525005577559493702993146807225361802167453489706384599072968062876158429907012794678374658052643106492832613851482088831697361117116847494275586263398055786306997629067970379802849648646327859385531315664221468756764866886951692283707932355333236655329299712264094434683517280694022189893587667362650855838281842572281093171232811366406220205355295423089611775315545429433386445430577991145354086222311974923494584494660778159201801527984393452312011041402180026454479649749840473191709867980992421153643751017781167243483858922176229514871642512868026698260541803296655591135248452444860843530452035448493044821843401743444654141348587919408512474301187596807969350497021662658923356898941281384404004041832682137331985942105359826170544941869730520779719379573257688476051185944015742279589176177978515625 to get 1.

$$\frac{\lambda ^{2}-2}{3}+1+1$$

Add 1 and 1 to get 2.

$$\frac{\lambda ^{2}-2}{3}+2$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 2 times \frac{3}{3}.

$$\frac{\lambda ^{2}-2}{3}+\frac{2\times 3}{3}$$

Since \frac{\lambda ^{2}-2}{3} and \frac{2\times 3}{3} have the same denominator, add them by adding their numerators.

$$\frac{\lambda ^{2}-2+2\times 3}{3}$$

Do the multiplications in \lambda ^{2}-2+2\times 3.

$$\frac{\lambda ^{2}-2+6}{3}$$

Combine like terms in \lambda ^{2}-2+6.

$$\frac{\lambda ^{2}+4}{3}$$

Factor

$$\frac{\lambda ^{2}+4}{3}$$