a] (16² x 15³ x 5²) : ((40)⁶ x 3²) = ((2⁴)² x (3 x 5)³ x 5²) : ((2³ x 5)⁶ x 3²) = (2⁸ x 3³ x 5³ x 5²) : (2¹⁸ x 5⁶ x 3²) = 2⁸⁻¹⁸ x 3³⁻² x 5³⁺²⁻⁶ = 2⁻¹⁰ x 3¹ x 5⁻¹ = 3/(2¹⁰ x 5) = 3/(1024 x 5) = 3/5120
b] ((-20)² x (-5)⁵ x 10³) : (4⁹ x 25⁴) = (20² x -5⁵ x 10³) : ((2²)⁹ x (5²)⁴) = - ((2² x 5)² x 5⁵ x (2 x 5)³) : (2¹⁸ x 5⁸) = - (2⁴ x 5² x 5⁵ x 2³ x 5³) : (2¹⁸ x 5⁸) = - 2⁴⁺³⁻¹⁸ x 5²⁺⁵⁺³⁻⁸ = - 2⁻¹¹ x 5² = - 25/2¹¹ = - 25/2048
c] (49⁵ x 21³ x 6⁴) : 42⁸ = ((7²)⁵ x (3 x 7)³ x (2 x 3)⁴) : (2 x 3 x 7)⁸ = (7¹⁰ x 3³ x 7³ x 2⁴ x 3⁴) : (2⁸ x 3⁸ x 7⁸) = 7¹⁰⁺³⁻⁸ x 3³⁺⁴⁻⁸ x 2⁴⁻⁸ = 7⁵ x 3⁻¹ x 2⁻⁴ = 7⁵ / (3 x 2⁴) = 16.807 / 48
d] (2/3)⁴ x (1/4)³ x (9/2)² : (1/2)² = 2⁴ x 3⁻⁴ x (2⁻²)³ x 3⁴ x 2⁻⁴ x 2² = 2⁴⁻⁶⁻⁴⁺² x 3⁻⁴⁺⁴ = 2⁻⁴ x 3⁰ = 1/16
e] (-1/3)³ x (1/5)² x 30⁴ : 16² = - 3⁻³ x 5⁻² x (2 x 3 x 5)⁴ : ((2⁴)²) = - 3⁻³ x 5⁻² x 2⁴ x 3⁴ x 5⁴ x 2⁻⁸ = - 2⁴⁻⁸ x 3⁻³⁺⁴ x 5⁻²⁺⁴ = - 2⁻⁴ x 3¹ x 5² = - (3 x 25)/2⁴ = - 75/16
Verified answer
Bab EksponensialMatematika SMK Kelas X
a] (16² x 15³ x 5²) : ((40)⁶ x 3²) = ((2⁴)² x (3 x 5)³ x 5²) : ((2³ x 5)⁶ x 3²)
= (2⁸ x 3³ x 5³ x 5²) : (2¹⁸ x 5⁶ x 3²)
= 2⁸⁻¹⁸ x 3³⁻² x 5³⁺²⁻⁶
= 2⁻¹⁰ x 3¹ x 5⁻¹
= 3/(2¹⁰ x 5)
= 3/(1024 x 5)
= 3/5120
b] ((-20)² x (-5)⁵ x 10³) : (4⁹ x 25⁴) = (20² x -5⁵ x 10³) : ((2²)⁹ x (5²)⁴)
= - ((2² x 5)² x 5⁵ x (2 x 5)³) : (2¹⁸ x 5⁸)
= - (2⁴ x 5² x 5⁵ x 2³ x 5³) : (2¹⁸ x 5⁸)
= - 2⁴⁺³⁻¹⁸ x 5²⁺⁵⁺³⁻⁸
= - 2⁻¹¹ x 5²
= - 25/2¹¹
= - 25/2048
c] (49⁵ x 21³ x 6⁴) : 42⁸ = ((7²)⁵ x (3 x 7)³ x (2 x 3)⁴) : (2 x 3 x 7)⁸
= (7¹⁰ x 3³ x 7³ x 2⁴ x 3⁴) : (2⁸ x 3⁸ x 7⁸)
= 7¹⁰⁺³⁻⁸ x 3³⁺⁴⁻⁸ x 2⁴⁻⁸
= 7⁵ x 3⁻¹ x 2⁻⁴
= 7⁵ / (3 x 2⁴)
= 16.807 / 48
d] (2/3)⁴ x (1/4)³ x (9/2)² : (1/2)² = 2⁴ x 3⁻⁴ x (2⁻²)³ x 3⁴ x 2⁻⁴ x 2²
= 2⁴⁻⁶⁻⁴⁺² x 3⁻⁴⁺⁴
= 2⁻⁴ x 3⁰
= 1/16
e] (-1/3)³ x (1/5)² x 30⁴ : 16² = - 3⁻³ x 5⁻² x (2 x 3 x 5)⁴ : ((2⁴)²)
= - 3⁻³ x 5⁻² x 2⁴ x 3⁴ x 5⁴ x 2⁻⁸
= - 2⁴⁻⁸ x 3⁻³⁺⁴ x 5⁻²⁺⁴
= - 2⁻⁴ x 3¹ x 5²
= - (3 x 25)/2⁴
= - 75/16