Question

Plsss zad w załączniku dam naj i polubię prof

Answer 1

Odpowiedź:

6. q i r

3²⁴:3⁸=3¹⁶

(3⁵)⁶:(3⁹)³=3³⁰:3²⁷=3³

(3⁸*3¹⁰*3¹²):(3⁹*3¹¹*3¹³)=3³⁰:3³³=3-³

3³*3-³=3⁰=1

2.

(3:4)⁷*(2:3)⁷=((3:4)(2:3))⁷=(1:2)⁷

(-18)³:(-2)³=(-18:(-2))³=9³

((-0,6)³)⁵=(-0,6)¹⁵=-0,6¹⁵

Answer 2

Verified answer

Szczegółowe wyjaśnienie:

Potęgi

Korzystamy z praw potęgowania:

[tex]a^{m}\cdot a^{n} = a^{m+n}\\\\a^{m}:a^{n} = a^{m-n}\\\\a^{n}\cdot b^{n} = (a\cdot b)^{n}\\\\a^{n}:b^{n} = (a:b)^{n}\\\\(a^{m})^{n} = a^{m\cdot n}\\\\a^{0} = 1[/tex]

Ćwiczenie 2

[tex]b) \ (\frac{3}{4})^{7}\cdot(\frac{2}{3})^{7} = (\frac{3}{4}\cdot\frac{2}{3})^{7} =(\frac{2}{4})^{7} =\boxed{ \left(\frac{1}{2}\right)^{7}}[/tex]

[tex]c) \ (-18)^{3}:(-2)^{3} = [-18:(-2)]^{3} = \boxed{9^{3}}[/tex]

[tex]d) \ [(-0,6)^3]^{5} = (-0,6)^{3\cdot 5} = \boxed{(-0,6)^{15}}[/tex]

Ćwiczenie 6

[tex]p = 3^{24}:3^{8} =3^{24-8} = 3^{16}\\\\q = (3^{5})^{6}:(3^{9})^{3} = 3^{5\cdot6}:3^{9\cdot3} = 3^{30}:3^{27} = 3^{30-27} = \underline{3^{3}}\\\\r = \frac{3^{8}\cdot3^{10}\cdot3^{12}}{3^{9}\cdot3^{11}\cdot3^{13}} = \frac{3^{8+10+12}}{3^{9+11+13}} = \frac{3^{30}}{3^{33}} =3^{30-33} = \underline{3^{-3}}[/tex]

a⁰ = 1, zatem iloczyn q i r da nam 1:

[tex]q\cdot r = 3^{3}\cdot 3^{-3} = 3^{3+(-3)} = 3^{3-3} = 3^{0} = \underline{1}\\\\Odp. \ \boxed{q\cdot r = 1}[/tex]