Question

find the value of m​

Answer 1

Answer :-

$\boxed{\large \bf\underline{ \red{ m = 9}}}$

GIVEN :-

$\sf {( - 3)}^{m + 1} \times {( - 3)}^{ - 3} = {( - 3)}^{7}$

TO FIND :-

$: \implies \sf{\: value \: of \: m}$

SOLUTION :-

$\bf {( - 3)}^{m + 1} \times {( - 3)}^{ - 3} = {( - 3)}^{7}$

$\bf {( a)}^{m} \times {(b )}^{n } = {( a)}^{m + n}$

In this Question :-

$\sf \: a = ( -3 )$

$\sf \: m = m + 1$

$\sf n = - 3$

PUTTING VALUES :-

 

$\bf {( - 3)}^{(m + 1) + (- 3)} = {( - 3)}^{7}$

$\bf {( - 3)}^{m + 1 - 3} = {( - 3)}^{7}$

$\bf {( - 3)}^{m - 2} = {( - 3)}^{7}$

$\bf {( - 3)}^{m } = {( - 3)}^{7 + 2}$

$\sf {( - 3)}^{m} = {( - 3)}^{9}$

$\boxed{ \therefore \bf \red{ m = 9}}$

VERIFIACTION :-

$\boxed{\sf LHS = RHS}$

$\implies \sf {( - 3)}^{m + 1} \times {( - 3)}^{ - 3} = {( - 3)}^{7}$

$\implies\sf {( - 3)}^{9 + 1} \times {( - 3)}^{ - 3} = {( - 3)}^{7}$

$\implies \sf {( - 3)}^{10} \times {( - 3)}^{ - 3} = {( - 3)}^{7}$

$\implies \sf {( - 3)}^{10 - 3} = {( - 3)}^{7}$

$\implies \boxed{\sf\large\red{ {( - 3)}^{7} = {( - 3)}^{7} }}$

$\bf \therefore hence \:proved \:\boxed{\sf L.H.S= R.H.S}$

More exponential identity :-

$\bf 1.\:{a}^{m} \times {a}^{n} = {a}^{m + n}$

$\bf2.\: \frac{ {a}^{m} }{ {a}^{n} } = {a}^{m - n}$

$\bf 3.\:{a}^{0} = 1$

$\bf 4.\:{ ({a}^{m}) }^{n} = {a}^{mn}$