Question

Find the value of m for which
${7}^{m} \times {7}^{2} = {7}^{5}$
​

Answer 1

$\tt: \implies Required\:answer\:is\:3$

$\tt: \implies 7^{m} *7^{2} =7^{5} \\\tt: \implies In\:multiplication\:if\:bases\:are\:same\:then\:powers\:are\:added\\\tt: \implies so,\:7^{m+2} =7^{5} \\\tt: \implies As\:bases\:are\:same\:on\:both\:sides\:we\:can\:say\:that\:powers\:are\:are\:also\:same\\\tt: \implies Thus, \:m+2=5\\\tt: \implies m=5-2=3\\\tt: \implies m=3$

Hope my answer will help you :)