Question

find the value of m if (7)⁶×(7)⁷=(7)⁷m+³​

Answer 1

Answer:

$\large\bold\red{m=49}$

Step-by-step explanation:

Given,

${7}^{6} \times {7}^{7} = {7}^{7} \times {m}^{3}$

To find, m

We get,

$= > {7}^{6} \times \cancel{ {7}^{7}} = \cancel{ {7}^{7} } \times {m}^{3} \\ \\ = > {7}^{6} = {m}^{3}$

But,

We know that,

• ${x}^{ {y}^{a} } = {x}^{ay}$

Therefore,

We get,

$= > {m}^{3} = {( {7}^{2}) }^{3}$

Since the powers are same,

Therefore,

Bases will also be same,

Thus,

We get,

$= > m = {7}^{2} \\ \\ = > \bold{ m = 49}$