Question

find the value of x if (-2)power x+1 × (-2)power 3 =(-2)power 7​

Answer 1

ANSWER:

Given:

• $(-2)^{x+1}\times(-2)^3=(-2)^7$

To Find:

• Value of x

Solution:

We are given that,

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

Now, we know that,

⟹ a^m × a^n = a^(m+n)

This means, if we have a number, a, which has a power m, and is being multiplied by the same number, a, but with power, n. Then both the powers of the numbers will be added.

So,

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

$\implies(-2)^{(x+1)+(3)}=(-2)^7$

$\implies(-2)^{(x+1+3)}=(-2)^7$

$\implies(-2)^{x+4}=(-2)^7$

Now, we can see that at LHS as well as RHS, the bases are same. So, we'll use this,

If,

⟹ a^m = a^n

Then,

⟹ m = n

So,

$\implies(-2)^{x+4}=(-2)^7$

$\implies x+4=7$

Transposing 4 to RHS,

$\implies x=7-4$

Hence,

$\bf\implies x=3$

Therefore, the value of x is 3.

Answer 2

Answer:

X = 3

Hope this helps!!