Exponential battle between two years!

Algebra Level 1

$\Large{{\color{#20A900}{4}}^{\color{#3D99F6}{2020}}-{\color{#20A900}{4}}^{\color{#3D99F6}{2019}}= \color{#624F41}{?}}$

4^{2019} \times 2

4^{2018} \times 5

4^{2018} \times 3

4^{2019}

4^{2019} \times 3

3 solutions

Sin Ndt
Jul 3, 2020

$4^{2020}$ $-$ $4^{2019}$

= $4^{2019}$ x $4$ - $4^{2019}$ x $1$

= $4^{2019}$ x ( $4 - 1$ )

= $4^{2019}$ x $3$

In generality we also have:

$4^{n + 1}$ - $4^n$

= $4^{n}$ x $4$ - $4^{n}$ x $1$

= $4^{n}$ x ( $4 - 1$ )

= $4^{n}$ x $3$

AND:

$A^{n + 1}$ - $A^{n}$

= $A^{n}$ x $A$ - $A^{n}$ x $1$

= $A^{n}$ x ( $A - 1$ )

Vinayak Srivastava
Jul 1, 2020

$\Large{{\color{#20A900}{4}}^{\color{#3D99F6}{2020}}-{\color{#20A900}{4}}^{\color{#3D99F6}{2019}}= {\color{#20A900}{4}}^{\color{#3D99F6}{2019}} \times (4-1) =\boxed{{\color{#20A900}{4}}^{\color{#3D99F6}{2019}}\times 3 }}$

Great! But I don't understand where did you get the ( $4 - 1$ ) from?

Yajat Shamji - 11 months, 2 weeks ago

Well, $4^{2020}=4(4^{2019}),$ hence there is a $4$ .

Jeff Giff - 11 months, 2 weeks ago

Then where do you get the $- 1$ from in the ( $4 - 1$ )?

Yajat Shamji - 11 months, 2 weeks ago

@Yajat Shamji – @Yajat Shamji He took $4^{2019}$ common

Aaghaz Mahajan - 11 months, 2 weeks ago

@Aaghaz Mahajan – Ok. Thanks a lot. Now I understand.

Yajat Shamji - 11 months, 2 weeks ago

$4^{2020}-4^{2019}=\color{#D61F06}4\color{#333333}(4^{2019})\color{#3D99F6}-1\color{#333333}(4^{2019})=(\color{#D61F06}4\color{#3D99F6}-1\color{#333333})4^{2019}$ :)

Jeff Giff - 11 months, 2 weeks ago

@Jeff Giff – Ok. Thanks a lot. Now I understand.

Yajat Shamji - 11 months, 2 weeks ago

@Jeff Giff – A minor typo, you wrote $4^{2}019$ instead of $4^{2019}$

Aaghaz Mahajan - 11 months, 2 weeks ago

solve it with the same way

Razing Thunder - 11 months, 2 weeks ago

Lâm Lê
Sep 9, 2020

$\frac{4^{2020}}{4^{2019}}=4\Rightarrow4^{2020}-4^{2019}=\boxed{\color{#20A900}3×4^{2019}}\approx64 \text{ Duoquadrigentillion (Give or take a few)}$

Exponential battle between two years!

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