Question

Find the value of k if (-2)^k+1 × (-2)^3 = (-2)^7

Answer 1

$the \: value \: of \: k \: is \: \: 3$

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Answer 2

Question

Find the value of K

$\sf{ {( - 2)}^{k + 1} × (-2)^3 = (-2)^7}$

Concept

Here the concept of exponent and power is used.

when bases are same and multiplied then the powers get added.

$\sf{ {a}^{x} \times {a}^{y} = {a}^{x + y} }$

Solution

$\sf{ \to \: { ( - 2)}^{k + 1} \times {( - 2)}^{3} = {( - 2)}^{7} } \\ \\ \sf{ \to {( - 2)}^{k + 1 + 3} = {( - 2)}^{7} } \\ \\ \sf{ \to \: k + 4 = 7} \\ \\ \sf{ \to \: k = 3}$

so the value of K is 4

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More to know !!

$\sf{ \to {a}^{0} = 1} \\ \\ \sf{ \to {a}^{x} \times {a}^{y} = {a}^{x + y} } \\ \\ \sf{ \to \: \frac{ {a}^{x} }{ {a}^{y} } = {a}^{x - y} } \\ \\ \sf{ \to \: { ({a}^{m} )}^{n} = {a}^{m.n} }$

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