Question

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

Answer 1

Answer:

THE VALUE OF k IS -13/6

Step-by-step explanation:

(-2)(k+1)*(-2)3 = (-2)7

(-2k-2)*-6 = -14

12k+12=-14

12k=-14-12

12k=-26

k=-26/12

k= -13/6

I HOPE YOU UNDERSTOOD THE QUESTION

Answer 2

The value of k = 3

Given :

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

To find :

The value of k

Formula :

We are aware of the formula on indices that

$\sf {a}^{m} \times {a}^{ n} = {a}^{m + n}$

Solution :

Step 1 of 2 :

Write down the given equation

The given equation is

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

Step 2 of 2 :

Find the value of k

We use the formula

$\sf {a}^{m} \times {a}^{ n} = {a}^{m + n}$

Thus we get

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

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

$\displaystyle \sf{ \implies {( - 2)}^{k + 4} = {( - 2)}^{7} }$

$\displaystyle \sf{ \implies k + 4 = 7 }$

$\displaystyle \sf{ \implies k = 7 - 4 }$

$\displaystyle \sf{ \implies k = 3}$

The required value of k = 3

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