Question

find the value of m for which minus 3 to the power m + 1 into minus 3 to the power 5 equal to minus 3 to the power 7​

Answer 1

$expression ( - 3) {}^{m + 1} \times ( - 3) {}^{5} = ( - 3) {}^{7}$

We know ,

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

$( - 3) {}^{m + 1 + 5} = ( - 3) {}^{7}$

$( - 3) {}^{m + 6} = ( - 3) {}^{7}$

Comparing the power as bases are same,

$m + 6 = 7$

$m = 1$

Therefore, The value of m is 1.

Answer 2

$\huge\underline\mathrm{Question:-}$

• To find value of m.

$\huge\underline\mathrm{Solution:-}$

★ Given Expression -

$( { - 3}^{m + 1} ) \times { - 3}^{5} = { - 3}^{7}$

★ According to law of indices , This property exists in following way -

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

Converting the eqn -

$( { - 3}^{m + 1 + 5} ) = ( { - 3}^{7} )$

$( { - 3}^{m + 6}) = ( { - 3}^{7} )$

Here, Bases (-3) are same. So comparing the eqns.

$m + 6 = 7$

$m = 7 - 6$

$m = 1$

$\huge\underline\mathrm{Answer:-}$

• Value of m is 1.