Question

7) calcule os quocientes:
a) (-45xd⁵)÷(-9d)=
b) (72x⁴y)÷(-8x²y)=
c) (4/5m³)=(7/6m)=
d) (-8p⁷a⁵)÷(p⁵a²/4)=

8) calcule as potências:
a) (5x)³
b) (2/3x²)⁴
c) (m⁵y⁴/2)⁶
d) [(-2m³x⁴)²]²​

Answer 1

Resposta:

Explicação passo a passo:

7) calcule os quocientes:

a)

(-45xd⁵)÷(-9d) = -45xd⁽⁵⁻¹⁾/(-9) = 5xd⁴

b)

(72x⁴y)÷(-8x²y) = (72x⁽⁴⁻²⁾y⁽¹⁻¹⁾)/(-8) = -9x²y⁰ = -9x²

c)

(4/5m³)÷(7/6m) = (4/5).(6/7).m⁽³⁻¹⁾ = 24m²/35

d)

(-8p⁷a⁵)÷(p⁵a²/4) = (-8p⁷a⁵).(4/p⁵a²) = -32p⁽⁷⁻⁵⁾.a⁽⁵⁻²⁾ = -32p²a³

8) calcule as potências:

a)

(5x)³ = 5³.x³ = 5.5.5.x³ = 125x³

b)

(2/3x²)⁴ = 2⁴/(3x²)⁴ = 2.2.2.2/(3⁴.x⁽²ˣ⁴⁾) = 16/(3.3.3.3.x⁸) = 16/(81x⁸)

c)

(m⁵y⁴/2)⁶ = m⁽⁵ˣ⁶⁾y⁽⁴ˣ⁶⁾/2⁶ = m³⁰y²⁴/64

d)

[(-2m³x⁴)²]²​ = (-2m³x⁴)⁽²ˣ²⁾​ = (-2m³x⁴)⁴​ = (-2)⁴.m⁽³ˣ⁴⁾.x⁽⁴ˣ⁴⁾ = 16m¹²x¹⁶

Propriedades:

$(a^{m})^{n}=a^{m.n}\\\\\sqrt[n]{x^m} =x^{\frac{m}{n} }\\\\a^{m}a^{n}=a^{m+n}\\\\\frac{a^{m}}{a^{n}}=a^{m-n} \\\\a^{0}=1\\\\a^{1}=a$