Respuesta :

CHERLYNnotCHERRY

Answer:

The value of k is 1.

Step-by-step explanation:

You have to apply Indices Law :

[tex] {a}^{m} \times {a}^{n} = {a}^{m + n} [/tex]

For this question :

[tex] {( \frac{4}{5} )}^{2} \times {( \frac{4}{5} )}^{5} = {( \frac{4}{5} )}^{6k + 1} [/tex]

[tex] {( \frac{4}{5}) }^{2 + 5} = {( \frac{4}{5}) }^{6k + 1} [/tex]

[tex]by \: comparison[/tex]

[tex]2 + 5 = 6k + 1[/tex]

[tex]7 = 6k + 1[/tex]

[tex]7 - 1 = 6k[/tex]

[tex]6k = 6[/tex]

[tex]k = 6 \div 6[/tex]

[tex]k = 1[/tex]

devishri1977

Answer:

k = 1

Step-by-step explanation:

[tex]a^{m} * a^{n} = a^{m+n}\\\\(\frac{4}{5})^{2}*(\frac{4}{5})^{5}=(\frac{4}{5})^{6k+1}\\\\\\(\frac{4}{5})^{2+5}=(\frac{4}{5})^{6k+1}\\\\(\frac{4}{5})^{7}=(\frac{4}{5})^{6k+1}[/tex]

Compare the powers,

6k + 1 = 7         {subtract 1 from both sides}

     6k = 7 - 1

    6k  = 6     {Divide both sides by 6}

  6k/6= 6/6

k = 1

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