zad 1. Sprawdź prawdziwośc podanych równości:
a) (a²b)³ * b = a⁴b²(ab)²
b) a * (ab²) * b = (ab)² * b² / b
c) [(xy)²]⁴ / (y²)³ = (xy)² * x⁶
d) [(ab)³]⁴ / [(ab)³]³ = (ab)³
e) (y²)³ * (x²y)⁶ = [(xy)⁴]² * (x²)² * y⁴
f) x² * [(xy²)³]² = [(xy)²]² * (xy²)⁴
zad.2 Wskaż pary wyrażeń mające takie same wartości:
a) (a²b)³ * b
b) a * (ab²) * b
c) a⁴b² * (ab)²
d) [(ab)²]⁴ / (b²)³ b ≠(znak nierownosci) 0
e) (ab)² * a⁶
f) b * (ab²)²
g) a² * [(ab²)³]²
h) [(ab)²]² * (ab²)⁴
zad.3 Sprawdź prawdziwośc podanych równości:
a) [(ab)³]⁴ / [(ab)³]³ = (ab)³
b) [(ab³)²]³ * (a⁶)² = [(ab⁵)² * (a²)]⁴ * (b⁴)²
c) (y³)² * (x²y)⁶ = [(xy)²]⁴ * (x²)² * y⁴
d) [(x²)³ * x]² * (y¹⁶ / y²) = [(y²)³ * y³]² * (x¹⁶ / x²)
za wszystko lub wiekszosc daje naj...zle odpowiedzi zglaszam ..ma byc dobrze zrobione !:*
prosze xd
zad 1. Sprawdź prawdziwośc podanych równości:
a) (a²b)³ * b = a⁴b²(ab)²
L = (a²b)³ * b = a²b⁴
P = a⁴b²(ab)² = a⁶*b⁴
L≠ P
b) a * (ab²) * b = (ab)² * b² / b
L = a * (ab²) * b = a²*b³
P = (ab)² * b² / b = a²*b⁴:b¹ = a² *b³
L = P
c) [(xy)²]⁴ / (y²)³ = (xy)² * x⁶
L = [(xy)²]⁴ / (y²)³= ( x⁸*y⁸): y⁶ = x⁸*y²
P =(xy)² * x⁶= x⁸*y²
L=P
d) [(ab)³]⁴ / [(ab)³]³ = (ab)³
L = [(ab)³]⁴ / [(ab)³]³ = (a*b)¹²: (a*b)⁹ = (a*b)³
P = (ab)³
L =P
e) (y²)³ * (x²y)⁶ = [(xy)⁴]² * (x²)² * y⁴
L = (y²)³ * (x²y)⁶ = y⁶*x¹²*y⁶ = x¹²*y¹²= (x*y)¹²
P = [(xy)⁴]² * (x²)² * y⁴= x²*y⁸*x⁴*y⁴ = x⁶*y¹² = (x*y² )⁶
L ≠ P
f) x² * [(xy²)³]² = [(xy)²]² * (xy²)⁴
L = x² * [(xy²)³]² = x²*x⁶*y¹²= x⁸y¹²
P = [(xy)²]² * (xy²)⁴= x⁴*y⁴*x⁴*y⁸ = x⁸*y¹²
L =P
zad.2 Wskaż pary wyrażeń mające takie same wartości:
a) (a²b)³ * b = a⁶b⁴
b) a * (ab²) * b = a²*b³
c) a⁴b² * (ab)² = a⁶*b⁴
d) [(ab)²]⁴ / (b²)³ b ≠(znak nierownosci) 0
[(ab)²]⁴ :(b²)³= a⁴b⁸: b⁶ = a⁴*b²
e) (ab)² * a⁶= a²*b² *a⁶ = a⁸*b²
f) b * (ab²)² = b* a²*b⁴ = a²*b⁵
g) a² * [(ab²)³]² = a²*a⁶*b¹² = a⁸*b¹²
h) [(ab)²]² * (ab²)⁴= a⁴*b⁴*a⁴*b⁸ = a⁸*b¹²
Pary równe :
a = c , g = h
zad.3 Sprawdź prawdziwośc podanych równości:
a) [(ab)³]⁴ / [(ab)³]³ = (ab)³
L = [(ab)³]⁴ / [(ab)³]³ =(a*b)¹²: (a*b)⁹ = (a*b)³
P = (ab)³
L = P
b) [(ab³)²]³ * (a⁶)² = [(ab⁵)² * (a²)]⁴ * (b⁴)²
L = [(ab³)²]³ * (a⁶)² = a⁶ *b¹⁸*a¹² = a¹⁸*b¹⁸ =(a*b)¹⁸
P = [(ab⁵)² * (a²)]⁴ * (b⁴)² = a⁸*b⁴⁰ *a⁸*b⁸ = a¹⁶*b⁴⁸
L ≠ P
c) (y³)² * (x²y)⁶ = [(xy)²]⁴ * (x²)² * y⁴
L = (y³)² * (x²y)⁶ =y⁶*x¹²*y⁶ = x¹²*y¹² = (x*y)¹²
P = [(xy)²]⁴ * (x²)² * y⁴=(x*y)⁸*x⁴*y⁴ = (xy)⁸*(x*y)⁴ = (x*y)¹²
L = P
d) [(x²)³ * x]² * (y¹⁶ / y²) = [(y²)³ * y³]² * (x¹⁶ / x²)
L = [(x²)³ * x]² * (y¹⁶ / y²) = (x⁶*x)² *y¹⁴ = x¹⁴*y¹⁴ = (x*y)¹⁴
P = [(y²)³ * y³]² * (x¹⁶ / x²) = (y⁶*y³)²*x¹⁴ = y¹⁴*x¹⁴ = x¹⁴*y¹⁸
L ≠ P