Question

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Przedstaw w postaci jednej potęgi:

a)2⁴ * 4³ * 8²

b) 3⁻² * 9⁵ * 27⁻⁵

c) 6⁻¹ * 1/36³ * (1/216)²

d) 5³ * 125 * ( ⅕)² / 25⁻² * 625³

e) (0,1)⁻² * (0,01)⁻³ * (0,001)⁻⁴ / 1000000

Answer 1

a) 2⁴ * 4³ * 8² = 2⁴ * (2²)³  * (2³)² = 2⁴ * 2⁶ * 2⁶ = 2¹⁶

 

b) 3⁻² * 9⁵ * 27⁻⁵ = 3⁻² * (3²)⁵ * (3³)⁻⁵ = 3⁻² * 3 ¹⁰ * 3⁻¹⁵ = 3⁻⁷

 

c) 6⁻¹ * 1/36³ * (1/216)² = 6⁻¹ * (6⁻²)³ * (6⁻³)² = 6⁻¹ * 6⁻⁶ * 6⁻⁶ = 6⁻¹³ 

 

d) 5³ * 125 * ( ⅕)² / 25⁻² * 625³ = 5³ * 5³ * (5⁻¹)² / (5²)⁻² * (5⁴)³ = 

5⁶ * 5 ⁻² / 5⁻⁴ * 5¹² = 5⁴ / 5⁸ = 5⁻⁴

 

e) (0,1)⁻² * (0,01)⁻³ * (0,001)⁻⁴ / 1000000 =

(1/10)⁻² * (1/100)⁻³ * (1/1000)⁻⁴ / 10⁶ =

(10⁻¹)⁻² * (10⁻²)⁻³ * (10⁻³)⁻⁴ / 10⁶ =

10² * 10⁵ * 10¹²  / 10⁶ =

10¹⁹ / 10⁶ = 10⁷