Question

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

= (-2)7​

Answer 1

Answer:

k = 4

Step-by-step explanation:

(-2)k+1 × (-2)3  = (-2)7​

-2k + -6 = -14

- 2k = -14 + 6

- 2k = - 8

k = -8 / -2

k = 4

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Answer 2

The required value of k = 3

Given :

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

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

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

Step 2 of 2 :

Find the value of k

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

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

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

Comparing both sides we get

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

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

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

Hence the required value of k = 3

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