Question

Plz help. Attachment below

Answer 1

Answer:

The value of k is 1.

Step-by-step explanation:

You have to apply Indices Law :

${a}^{m} \times {a}^{n} = {a}^{m + n}$

For this question :

${( \frac{4}{5} )}^{2} \times {( \frac{4}{5} )}^{5} = {( \frac{4}{5} )}^{6k + 1}$

${( \frac{4}{5}) }^{2 + 5} = {( \frac{4}{5}) }^{6k + 1}$

$by \: comparison$

$2 + 5 = 6k + 1$

$7 = 6k + 1$

$7 - 1 = 6k$

$6k = 6$

$k = 6 \div 6$

$k = 1$

Answer 2

Answer:

k = 1

Step-by-step explanation:

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

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