Espressione con potenze

[18¹ x  (18⁴ × 18¹)³]²:[3⁰× (3⁷ × 3¹)²]²

Potenze con la stessa base, nella moltiplicazione si sommano gli esponenti;

[18^1 x (18^5)^3]^2 : [1 x (3^8)^2]^2 =

Potenza di potenza: si moltiplicano tra loro gli esponenti.

= [18^1 x 18^15]^2 : [3^16]^2 =

= [18^16]^2 : [3^32] =

= 18^32 : 3^32; 

potenze con basi diverse, ma stesso esponente: possiamo dividere le basi, l'esponente resta 32;

= (18 : 3)^32 = 6^32.

Ciao @lize_iquin

(18^1·(18^5)^3)^2/(1·(3^8)^2)^2=

=(2^16·3^32)^2/3^32=

=2^32·3^64/3^32=

=2^32·3^32=

=6^32

[18¹×(18⁴×18¹)³]² : [3⁰×(3⁷×3¹)²]²

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$\small \dfrac{\left[18^1×\left(18^4×18^1\right)^3\right]^2}{\left[3^0×\left(3^7×3^1\right)^2\right]^2} = $

$\small = \dfrac{\left[18×\left(18^{4+1}\right)^3\right]^2}{\left[1×\left(3^{7+1}\right)^2\right]^2} = $

$\small = \dfrac{\left[18×\left(18^5\right)^3\right]^2}{\left[\left(3^8\right)^2\right]^2} = $

$\small = \dfrac{\left[18×18^{5×3}\right]^2}{\left[3^{8×2}\right]^2} = $

$\small = \dfrac{\left[18×18^{15}\right]^2}{\left[3^{16}\right]^2} = $

$\small = \dfrac{\left[18^{1+15}\right]^2}{3^{16×2}} = $

$\small = \dfrac{\left[18^{16}\right]^2}{3^{32}} = $

$\small = \dfrac{18^{16×2}}{3^{32}} = $

$\small = \dfrac{18^{32}}{3^{32}} = $

$\small = \left(\dfrac{\cancel{18}^6}{\cancel3_1}\right)^{32} = $

$\small = 6^{32} $

[ 18^1* (18^5)^3 ]^2 : [1*(3^8)^2]^2 ?

= [18*18^15]^2 : 3^(8*2*2) =

= 18^(16*2) : 3^32 =

= 18^32 : 3^32 =

= (18:3)^32 =

= 6^32