Question

(2^9)^2•4^9 =. va rog e urgent dau coroana
8^24:16^18=
125^9:25^13=
81^15:27^20=
8^13:64^84=
3^72:81^12=

Answer 1

Răspuns:

Explicație pas cu pas:

(2⁹)²· 4⁹ = 2⁹ˣ²·(2²)⁹ = 2¹⁸·2²ˣ⁹ = 2¹⁸·2¹⁸ = 2¹⁸⁺¹⁸ = 2³⁶

8²⁴ : 16¹⁸ = (2³)²⁴ : (2⁴)¹⁸ = 2³ˣ²⁴ :2⁴ˣ¹⁸ = 2⁷²:2⁷² = 2⁷²⁻⁷²=2⁰=1

81¹⁵ : 27²⁰ = (3⁴)¹⁵ :(3³)²⁰ = 3⁴ˣ¹⁵ : 3³ˣ²⁰ = 3⁶⁰ : 3⁶⁰ = 3⁰ = 1

8¹³ : 64⁸⁴ = (2³)¹³ :(2⁶)⁸⁴ = 2³ˣ¹³ : 2⁶ˣ⁸⁴ = 2³⁹ : 2⁵⁰⁴ = 2³⁹⁻⁵⁰⁴ =

= 2⁻⁴⁶⁵ = (1/2)⁴⁶⁵

3⁷² : 81¹² = 3⁷² : (3⁴)¹² = 3⁷² : 3⁴ˣ¹² = 3⁷² : 3⁴⁸ = 3⁷²⁻⁴⁸ = 3²⁴

Mai era unul :

125⁹ : 25¹³ = (5³)⁹ :(5²)¹³ = 5³ˣ⁹ : 5²ˣ¹³ = 5²⁷:5²⁶ = 5²⁷⁻²⁶ = 5¹ = 5

Answer 2

Răspuns:

$\it (2^9)^2\cdot 4^9=2^{9\cdot2}\cdot(2^{2})^{9}=2^{18}\cdot 2^{2\cdot9} =2^{18}\cdot2^{18}=2^{18+18}=\boxed{\it2^{36}}$

$\it (8)^{24}: 16^{18}=(2^{3})^{24}:(2^{4})^{18}=2^{3\cdot24}: 2^{4\cdot18} =2^{72}:2^{72}=\boxed{\it1}}$

$\it 125^{9}:25^{13}=(5^{3})^{9}:(5^{2})^{13}=5^{3\cdot9}:5^{2\cdot13}=5^{27}:5^{26}=5^{27-26}=\boxed{\it 5}$

$\it 81^{15}:27^{20}=(3^{4})^{15}:(3^{3})^{20}=3^{4\cdot15}:3^{3\cdot20}=3^{60}: 3^{60}=\boxed{\it 1}$

$\it 8^{13}:64^{84} = 8^{13}:(8^{2})^{84}=8^{13}:8^{168}=8^{13-168}=8^{-155}=\boxed{\it \dfrac{1}{8^{155}}}$

$\it 3^{72}:81^{12}=3^{72}:(3^{4})^{12}=3^{72}:3^{4\cdot12}=3^{72}:3^{48}=3^{72-48}=\boxed{\it 3^{24} }$