Question

ans me fast plz
ans with explanation ​

Answer 1

Answer:

k = 3

You can verify..

PLEASE MARK AS BRAINLIEST..

Answer 2

$\large \mathtt{question} \\ \\ \large \mathtt{( { - 2)}^{k + 1} \times ( - {2)}^{3} = ( - {2)}^{7} }$

$\large \mathtt{ \: we \: \: know} \\ \\ \large \mathtt{ in \: \: multiplication : } \\ \\ \large \mathtt{when \: \: the \: \: bases \: \: are \: \: same } \\ \large \mathtt{the \: \: powers \: \: are \: \: added. }$

$\large \mathtt{( { - 2)}^{k + 1} \times ( - {2)}^{3} = ( - {2)}^{7} } \\ \\ : \large \implies \mathtt{( { - 2)}^{k + 1 + 3}= ( - {2)}^{7} } \\ \\ : \large \implies \mathtt{( { - 2)}^{k + 4}= ( - {2)}^{7} }$

$\large \mathtt{since.} \\ \large \mathtt{ \: \: bases \: \: are \: \: same} \\ \large \mathtt{ \rightarrow \: so \: \: powers \: \: can \: \: be \: \: equated}$

$\large \mathtt{( - {2})^{k + 4} = ( - {2)}^{7}} \\ \\ \large \: \: \: \: \: \: : \implies \mathtt{k + 4 = 7} \\ \\ \large \: \: \: \: \: \: \mathtt{on \: \: transposing \: \: terms : } \\ \\ \large : \implies \mathtt{k = 7 - 4} \\ \\ \large \therefore \: \: \underline{ \underline \mathtt{k = 3} }$

$\large \mathtt{ checking \: \: value \: \: of \: \: k : }$

$\large \mathtt{question} \\ \\ \large \mathtt{( { - 2)}^{k + 1} \times ( - {2)}^{3} = ( - {2)}^{7} }$

$\large \implies\mathtt{( { - 2)}^{3 + 1} \times ( - {2)}^{3} = ( - {2)}^{7} } \\ \\ \large \implies\mathtt{( { - 2)}^{4 } \times ( - {2)}^{3} = ( - {2)}^{7} }$

$\large \mathtt{ \: we \: \: know} \\ \\ \large \mathtt{ in \: \: multiplication : } \\ \\ \large \mathtt{when \: \: the \: \: bases \: \: are \: \: same } \\ \large \mathtt{the \: \: powers \: \: are \: \: added. }$

$\large \implies\mathtt{( { - 2)}^{4 + 3} = ( - {2)}^{7} } \\ \\ \large \therefore \: \: \underline { \underline\mathtt{( { - 2)}^{7} = ( - {2)}^{7} }}$

$\: \: \: \: \: \large \mathtt{l.h.s = r.h.s} \\ \\ \: \: \: \: \: \large \mathtt{ \: \: \: \: hence \: \: proved}$