Question

Oblicz:

2⁸² : 4⁴⁰

18⁴ / 9⁴

(5²)³ · 2⁶

0,01¹² · 100³

5⁸ : (0,2)⁻⁷

(121²)³ / (¹₁₁)⁻⁸ ·11⁻²

Uprość wyrażenie:

a) a⁶ · (a²)⁻³
b) (a/b)⁵ · a⁻² / (ba)²

Answer 1

1.

2^82 : 4^40 = 2^82 : (2^2)^40 = 2^82 : 2^80 = 2^2 = 4

 

18^4/9^4 = (18/9)^4 = 2^4 = 16

 

(5^2)^3 * 2^6 = 5^6 * 2^6 = (5*2)^6 = 10^6 = 1 000 000

 

0,01^12 * 100^3 = (1/100)^12 * 100^3 = 100^-12 *100^3 = 100^-9 = 1 *10^-8

 

5^8 :(0,2)^-7 = 5^8 :(2/10)^-7 = 5^8 :(1/5)^-7 = 5^8 : 5^7 = 5

 

(121^2)^3/(1/11)^-8 *11^-2 = [(11^2)^2]^3/11^8 *11^-2 = 11^12/11^6 = 11^6

 

2. 

a)

a^6 *(a^2)^-3 = a^6 * a^-6 = a^0 = 1

b)

(a/b)^5 *a^-2/(ba)^2 = a^5/b^5 *a^-2/a^2 *b^2 = a^3/b^5 *1/(a^2*b^2) = a/b^7