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9. Degrees of single prime numbers

Here are the degrees of prime numbers that are often used:

$n$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$2^{n}$	$2$	$4$	$8$	$16$	$32$	$64$	$128$	$256$	$512$	$1024$
$3^{n}$	$3$	$9$	$27$	$81$	$243$	$729$	-	-	-	-
$5^{n}$	$5$	$25$	$125$	$625$	-	-	-	-	-	-
$7^{n}$	$7$	$49$	$343$	-	-	-	-	-	-	-

Example:

Calculate

$7^{2} - 2^{5}$ .

The first step is always exponentiation.

$\begin{array}{l} 7^{2} = 49; \\ 2^{5} = 32 . \end{array}$

Substituting the found values, we obtain:

$7^{2} - 2^{5} = 49 - 32 = 17$ .

Consider examples of degrees with negative bases:

$\begin{array}{l} {(- 3)}^{2} = (- 3) \cdot (- 3) = 9; \\ {(- 3)}^{3} = (- 3) \cdot (- 3) \cdot (- 3) = - 27; \\ {(- 3)}^{4} = (- 3) \cdot (- 3) \cdot (- 3) \cdot (- 3) = 81 . \end{array}$

Important!

An even degree of a negative number is positive; an odd one is negative.

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9. Degrees of single prime numbers

Theory: