Question

cit va fi  6⁻¹⁰  pe  81⁻²·32⁻²

Answer 1

6^-10=1/6^10
32^-2=1/32²
81^-2=1/81²
exercitiul devine
81²/6^10x1/32²=(3^4)²/(2.3)^10x1/(2^5)2=3^8/2^10.3^10x1/2^10=1/(2^20.3²)=2^(-20).3^(-2)
^-puterea daca avem ^-2 inseamna ca este la puterea -2
.sau x-inmultire 
atunci exercitiul devine

(81².32²)/6^10=3^8.2^10/2^10.3^10=1/3^2=1/9

Answer 2

$\dfrac{6^{-10}}{81^{-2}\cdot32^{-2}}=\dfrac{81^2\cdot32^2}{6^{10}}=\dfrac{(3^4)^2\cdot(2^5)^2}{(3\cdot2)^{10}}=\dfrac{3^8\cdot2^{10}}{3^{10}\cdot2^{10}}=\dfrac{1}{3^2}=3^{-2}=\dfrac19$

Am folosit formula

$a^{-n}=\dfrac{1}{a^n}$, care se poate scrie si $\dfrac{1}{a^{-n}}=a^n$