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Evaluate-and-leave-your-answer-in-exponent-form-5-2024-5-2023-5-2022-5-2021-5-2020-5-2019-




Question Number 208508 by Tawa11 last updated on 17/Jun/24
Evaluate and leave your answer in exponent form.  5^(2024)  −  5^(2023)   −  5^(2022)   −  5^(2021)   −  5^(2020)   −  5^(2019)   =  ?
$$\mathrm{Evaluate}\:\mathrm{and}\:\mathrm{leave}\:\mathrm{your}\:\mathrm{answer}\:\mathrm{in}\:\mathrm{exponent}\:\mathrm{form}. \\ $$$$\mathrm{5}^{\mathrm{2024}} \:−\:\:\mathrm{5}^{\mathrm{2023}} \:\:−\:\:\mathrm{5}^{\mathrm{2022}} \:\:−\:\:\mathrm{5}^{\mathrm{2021}} \:\:−\:\:\mathrm{5}^{\mathrm{2020}} \:\:−\:\:\mathrm{5}^{\mathrm{2019}} \:\:=\:\:? \\ $$
Answered by mr W last updated on 17/Jun/24
=(5^5 −5^4 −5^3 −5^2 −5−1)×5^(2019)   =(5^5 −((5^5 −1)/(5−1)))×5^(2019)   =(((3×5^5 +1)/4))×5^(2019)   =2344×5^(2019)
$$=\left(\mathrm{5}^{\mathrm{5}} −\mathrm{5}^{\mathrm{4}} −\mathrm{5}^{\mathrm{3}} −\mathrm{5}^{\mathrm{2}} −\mathrm{5}−\mathrm{1}\right)×\mathrm{5}^{\mathrm{2019}} \\ $$$$=\left(\mathrm{5}^{\mathrm{5}} −\frac{\mathrm{5}^{\mathrm{5}} −\mathrm{1}}{\mathrm{5}−\mathrm{1}}\right)×\mathrm{5}^{\mathrm{2019}} \\ $$$$=\left(\frac{\mathrm{3}×\mathrm{5}^{\mathrm{5}} +\mathrm{1}}{\mathrm{4}}\right)×\mathrm{5}^{\mathrm{2019}} \\ $$$$=\mathrm{2344}×\mathrm{5}^{\mathrm{2019}} \\ $$
Commented by Tawa11 last updated on 17/Jun/24
Thanks sir.  I appreciate.
$$\mathrm{Thanks}\:\mathrm{sir}. \\ $$$$\mathrm{I}\:\mathrm{appreciate}. \\ $$

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