Question

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

Answer 1

Answer:

3

Step-by-step explanation:

(-2)^k+1 × (-2)^3 = (-2)^7

a^m × a^n = a^m+n

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

(-2)^k+4 = (-2)^7

if bases are equal then powers are also equal

k+4=7

k=7-4

k=3

Answer 2

Given,

An expression: (-2)^k+1×(-2)^3=(-2)^7

To find,

The value of k.

Solution,

We can simply solve this mathematical problem using the following process:

Mathematically,

For any variables x, a, and b,

(x)^a÷(x)^b = (x)^(a-b)

{Statement-1}

Now, according to the question;

(-2)^k+1×(-2)^3=(-2)^7

=> (-2)^(k+1) = (-2)^7÷(-2)^3

=> (-2)^(k+1) = (-2)^(7-3)

{according to statement-1}

=> (-2)^(k+1) = (-2)^4

On comparing both sides, we get;

=> (k+1) = 4

=> k = 4-1

=> k = 3

Hence, the value of k is equal to 3.