Question

(-2)^3 × (-2)^-6 = (-2)^2x-1 find the value of x​

Answer 1

Answer:

x= -1

Step-by-step explanation:

by using rule of powers and exponents,

L.H.S:

(-2)^3*(-2)^-6=(-2)^(3-6)

which is , (-2)^-3

now since the bases of both LHS and RHS are equal,

we can equate the powers,

which implies that, -3=2x-1

solving the equation, x= -1

Answer 2

Given,

• $(-2)^3 * (-2)^{-6} = (-2)^{2x-1}$ is given.

To find,

• We have to find the value of x.

Solution,

We can simply find the value of x by using the laws of exponents.

              $(-2)^3 * (-2)^{-6} = (-2)^{2x-1}$

   Using $a^m * a^n = a^{m+n}$, we get

                       $(-2)^{3-6} = (-2)^{2x-1}$

                        $(-2)^{-3} = (-2)^{2x-1}$

As we know, the same bases have the same powers, then equating the powers, we get

                            -3 = 2x-1

Transposing -1 from RHS to LHS, we get

                        -3 +1 = 2x

                            -2  = 2x

                         -2/2  = x

                             -1   = x

Hence, the value of x is -1 for $(-2)^3 * (-2)^{-6} = (-2)^{2x-1}$.