Respuesta :

xKelvin

Answer:

See Below.

Step-by-step explanation:

We have the expression:

[tex]5^5-5^4+5^3[/tex]

And we want to prove that it is divisible by 7.

To do so, we can factor out a 5³ from the expression. This yields:

[tex]=5^3(5^2-5^1+1)[/tex]

Simplify the parentheses:

[tex]=5^3(25-5+1)=5^3(21)[/tex]

We can see that the resulting expression is a value being multiplied by 21.

Since 21 is divisible by 7, our original expression must also be divisible by 7.

Hence proven.

Nayefx

Answer:

SEE BELOW

Step-by-step explanation:

to understand this

you need to know about:

  • PEMDAS

given:

  • [tex] \displaystyle \sf\frac{ {5}^{5} - {5}^{4} + {5}^{3} }{7} [/tex]

let's solve:

  1. [tex] \sf \: factor \: out \: {5}^{3} : \\ \displaystyle \sf\frac{ {5}^{3}( {5}^{2} - {5}^{} + 1) }{7} [/tex]
  2. [tex] \sf simlify \: parentheses \{squre \} : \\ \sf \frac{ {5}^{3} (25 - 5 + 1)}{7} [/tex]
  3. [tex]\sf simlify \: parentheses \{addition \} : \\ \sf \frac{ {5}^{3} (25 - 4)}{7} [/tex]
  4. [tex]\sf simlify \: parentheses \{substraction \} : \\ \sf \frac{ {5}^{3} (21)}{7} [/tex]
  5. [tex] \sf \: cancel \: 7 \: and \: 21 : \\ \frac{ {5}^{3} \cancel{(21) } \ ^{3} }{ \cancel{ \: 7 \: }} [/tex]
  • we can see 21 is divided by 7 therefore our original expression must also be divisible by 7

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