Question

(-2)^m+1 × (-2)^4 = (-2)^6 ⇒ m =?

Answer 1

We have been given an equation $(-2)^{m+1} \times (-2)^4 = (-2)^6$ and with this information, we have been asked to find out the value of 'm'.

Let's solve the equation and understanding the steps to get our final result.

$\implies (-2)^{m+1} \times (-2)^4 = (-2)^6$

Seperate a constant term part from a part containing the unknown among exponents,

$\implies (-2)^{1} (-2)^{m} (-2)^4 = (-2)^6$

Arrange the term to substitute the exponential equation,

$\implies (-2)^{1} (-2)^{m} (-2)^4 = (-2)^6$

Substitute $(-2)^m$ with $M$,

$\implies (-2)^{1} M (-2)^4 = (-2)^6$

Expand the expression,

$\implies -32M = (-2)^6$

Solve the solution to $M$,

$\implies M = -2$

Substitute $M$ with $(-2)^m$,

$\implies (-2)^m = -2$

Unify the base of exponential functions,

$\implies (-2)^m = (-2)^1$

The base of the exponent is the same,

$\implies \boxed{m = 1}$

Hence, the value of m is 1.