Question

solve[(-3/2power2)]power-3​

Answer 1

Solution :-

We have to solve :-

$\left(\dfrac{-3}{2^2}\right)^{-3}$

Now before solving we must know :-

♦ What is xⁿ ?

» It is the multiplication of "x" itself n times .

♦ Is (-x)ⁿ positive or negative ?

» To understand this let us consider this

let's take a number -1 ,

(-1)¹ = -1

(-1)² = (-1)(-1) = 1

(-1)³ = (-1)(-1)(-1) = -1

(-1)⁴ = (-1)(-1)(-1)(-1) = 1

So we can conclude that

When n = Even , the output will be positive.

When n = Odd , the output will be negative.

♦ What is x⁻ⁿ ?

» The x⁻ⁿ = $\dfrac{1}{x^n}$

Now coming back to the question :-

$\left(\dfrac{-3}{2^2}\right)^{-3}$

Solving the power of 2

$= \left(\dfrac{-3}{4}\right)^{-3}$

Making the indices positive :-

$= \left(\dfrac{4}{-3}\right)^{3}$

Now solving further :-

$= \dfrac{4^3}{-3^3}$

$= \dfrac{64}{-27}$

$= \dfrac{-64}{27}$

$\boxed{\boxed{\textsf{So Answer} = \it{\dfrac{-64}{27}}}}$