Question

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9/22

a) 4⁵ * 5⁶ =

b) (³₅)⁵ * (⁵₃)⁶=

c) (⁴₉)⁷ : (²₉)⁸=

d) (1⁴₉)⁵ : (4¹₃)⁴=

Proszę o rozpisanie wyników! tylko szybko, proszę!

Answer 1

a) 4⁵ * 5⁶ =

=  4^5 * 5^5 *5 =

= (4*5)^5  *5 =

=  5*20^5

 

b) (³₅)⁵ * (⁵₃)⁶=

= (3/5)^5 *(3/5)^(-6)=

= (3/5)^(-1) =

= (5/3)^ 1

= 5/3

 

c) (⁴₉)⁷ : (²₉)⁸=

= (4/9)^7  : (2/9)^8 =

= (4^7/ 9^7 ) : ( 2^8 : 9^8 )=

= [(4^7)*(9^8)] : [(9^7)*(2^8)]=

= [2^14)*(9^8)] : [(9^7)*(2^8)] =

= [ 2^14) : (2^8)]* [( 9^8) : (9^7 )] =

= [ 2^6] *[ 9^1] =

= 9* 2^6=

= 9*64 =

= 576

 

d) (1⁴₉)⁵ : (4¹₃)⁴=

=( 13/9)^5 : ( 13/3)^4 =

= [ ( 13^5 : 9^5] *[ 3^4 :13^4]=

= [13^5 : 13^4] *[3^4 : 9^5]=

= [ 13^1 ] *[ 3^4 : (3^2)^5] =

=  13*[ 3^4 : 3^10] =

= 13*[ 3^(-6) ]=

= 13*3^(-6)=

=13* (1/729) =

= 13/729

 

3^ (-6) - ozn. 3 do potęgi -6