Question

Find the value of M please help​

Answer 1

Step-by-step explanation:

$i) \:{ ( \frac{3}{7} )}^{ - 6} \times {( \frac{3}{7} )}^{10} = {( \frac{3}{7} )}^{2m}$

Since,

${a}^{x} \times {a}^{y} = {a}^{x + y}$

Hence,

$\:{ ( \frac{3}{7} )}^{ - 6 + 10} = {( \frac{3}{7} )}^{2m}$

As, the bases are same,

Therefore ,

- 6 + 10 = 2m

=> 4 = 2m

=> m = 4 ÷ 2

=> m = 2 (Ans)

$ii) \: {( \frac{2}{9} )}^{4} \times {( \frac{2}{9}) }^{ - 7} = {( \frac{2}{9} )}^{2m + 1}$

Since,

${a}^{x} \times {a}^{y} = {a}^{x + y}$

Hence,

$\:{ ( \frac{2}{9} )}^{ 4 + ( - 7)} = {( \frac{2}{9} )}^{2m + 1}$

As, the bases are same,

Therefore,

4 + (-7) = 2m + 1

=> - 3 = 2m + 1

=> - 3 - 1 = 2m

=> 2m = -4

=> m = -4 ÷ 2

=> m = - 2 (Ans)