### Theory:

The power operation is recorded as follows:

- base;

- exponent;

- the result of the increment or the value of the degree

Read as: "$$a$$ to the power $$b$$ equals $$c$$".

Calculating a step value is called stepping!

If the magnifier is a natural number.
$\begin{array}{l}{a}^{n}=\underset{⏟}{a\cdot a\cdot a\cdot ...\cdot a}\\ \phantom{\rule{2.940em}{0ex}}n\phantom{\rule{0.147em}{0ex}}\mathit{times}\end{array}$
The positive value of a positive integer is always positive.
${3}^{2}=3\cdot 3=9$

${\left(\frac{2}{5}\right)}^{3}=\frac{2}{5}\cdot \frac{2}{5}\cdot \frac{2}{5}=\frac{8}{125}$
A negative number is positive if the multiplier is an even number and negative if the multiplier is an odd number.
${\left(-3\right)}^{4}=\left(-3\right)\cdot \left(-3\right)\cdot \left(-3\right)\cdot \left(-3\right)=81$

${\left(-3\right)}^{3}=\left(-3\right)\cdot \left(-3\right)\cdot \left(-3\right)=-27$

Important!
Distinguish some seemingly similar notes ${\left(-2\right)}^{4}$ and $-{2}^{4}$. In the first case, the minus sign is the base sign $$(-2)$$ and in the second case, the degree sign (base is $$2$$).
${\left(-2\right)}^{4}=\left(-2\right)\cdot \left(-2\right)\cdot \left(-2\right)\cdot \left(-2\right)=16$

${-2}^{4}=-\left(2\cdot 2\cdot 2\cdot 2\right)=-16$.