Question

Am nevoie urgent!!! Dau coroana si 100 pt
!!! ​

Answer 1

Explicație pas cu pas:

18.

${( {2}^{x} )}^{10} = {2}^{60} \iff {2}^{10x} = {2}^{60} \\ 10x = 60 \implies \bf x = 6$

${( {4}^{6} )}^{20} = {2}^{40x} \iff {( {2}^{2} )}^{120} = {2}^{40x} \\ {2}^{240} = {2}^{40x} \iff 40x = 240 \\ \implies \bf x = 6$

${7}^{15} = {28}^{15} : {x}^{15} \iff {x}^{15} \cdot {7}^{15} = {(7 \cdot 4)}^{15} \\ {x}^{15} \cdot {7}^{15} = {7}^{15} \cdot {4}^{15} \iff {x}^{15} = {4}^{15} \\ \implies \bf x = 4$

${(42 : x)}^{25} = {7}^{25} \iff {42}^{25} : {x}^{25} = {7}^{25} \\ {42}^{25} = {7}^{25} \cdot {x}^{25} \iff {(7 \cdot 6)}^{25} = {7}^{25} \cdot {x}^{25} \\ {7}^{25} \cdot {6}^{25} = {7}^{25} \cdot {x}^{25} \iff {6}^{25} = {x}^{25} \\ \implies \bf x = 6$

19.

a)

${2}^{15} \cdot {8}^{10} \cdot {4}^{21} = {2}^{15} \cdot {( {2}^{3} )}^{10} \cdot {( {2}^{2} )}^{21} = {2}^{15} \cdot {2}^{3 \cdot 10} \cdot {2}^{2 \cdot 21} = {2}^{15} \cdot {2}^{30} \cdot {2}^{42} = {2}^{15 + 30 + 42} = \bf {2}^{87}$

b)

25⁶×125³×5¹¹ = (5²)⁶×(5³)³×5¹¹ = 5¹²×5⁹×5¹¹ = 5³²

c)

9⁷×27³×3¹³ = (3²)⁷×(3³)³×3¹³ = 3¹⁴×3⁹×3¹³ = 3³⁶

d)

${a}^{5} \cdot {(a \cdot b)}^{5} \cdot {b}^{5} = {a}^{5} \cdot {a}^{5} \cdot {b}^{5} \cdot {b}^{5} = {a}^{5 + 5} \cdot {b}^{5 + 5} = \bf {a}^{10} \cdot {b}^{10}$

e)

${27}^{8} : {81}^{2} \cdot {3}^{21} = {( {3}^{3} )}^{8} : {( {3}^{4} )}^{2} \cdot {3}^{21} = {3}^{24} : {3}^{8} \cdot {3}^{21} = {3}^{24 - 8} \cdot {3}^{21} = {3}^{16} \cdot {3}^{21} = {3}^{16 + 21} = \bf {3}^{37}$

f)

${36}^{5} \cdot {6}^{5} \cdot {6}^{x} = {( {6}^{2} )}^{5} \cdot {6}^{5} \cdot {6}^{x} = {6}^{10} \cdot {6}^{5} \cdot {6}^{x} = {6}^{10 + 5 + x} = \bf {6}^{15 + x}$