How to solve $(\frac{1}{x})^2x=e^6$?

Question

I need to solve this:

$$\left(\frac{1}{x}\right)^2x=e^6$$

I know it's equal

$$\ x=\frac{1}{e^6}$$

But how?

Answer 1

Hint. Note that $$ \left(\frac 1x\right)^2\cdot x = \frac{x}{x^2} = \frac 1x. $$

Answer 2

$$\left(\frac{1}{x}\right)^2x=\frac1x=e^6$$ $$x=\frac1{e^6}$$

Answer 3

$$\left(\frac{1}{x}\right)^2\cdot x=e^6\Longleftrightarrow$$ $$\frac{1^2}{x^2}\cdot x=e^6\Longleftrightarrow$$ $$\frac{1}{x^2}\cdot x=e^6\Longleftrightarrow$$ $$\frac{x}{x^2}=e^6\Longleftrightarrow$$ $$\frac{\frac{x}{x}}{\frac{x^2}{x}}=e^6\Longleftrightarrow$$ $$\frac{1}{x}=e^6\Longleftrightarrow$$ $$x=\frac{1}{e^6}$$

Answer 4

$$ \left(\frac{1}{x}\right)^2x=e^6 $$ Take the L.H.S and simplify it. $$ \text {L.H.S} = \left (\frac {1}{x}\right)^2x $$
$$ \text {L.H.S} = \left (\frac {1^2}{x^2} \right)x $$ $$ \text {Because,} \ 1^2 = 1 \ \text{and} \\ {x \over x^2} = {1 \over x} \ \text {then},\\ \left(\frac {1^2}{x^2} \right).x = { x \over x^2} = {1 \over x} = \ \text {L.H.S} $$ $$ \text {Because L.H.S = R.H.S} \\ \text{Then,} \\ {1 \over x } = e^6 \\ x = {1 \over e^{6}} $$