Question

oblicz:

1. 4⁻¹·(⅛)⁻²·64³=

2.

3.

Answer 1

1)

...=(2²)⁻¹ * (2⁻³)⁻² * (2⁶)³ = 2⁻² * 2⁶ * 2¹⁸ = 2⁻²⁺⁶⁺¹⁸ = 2 ²² = 4194304

 

2)

... = 3 ³/²   :  3¹/² = 3³/² ⁻ ¹/² = 3²/²=3¹=3

 

3)

  7                     7^√5 * 7^5        7 * 7^5                       7^6

-------------------- * ------------------=  --------------------------- = --------------------= 7^(3  1/6) = 7^19/6 = ⁶√7¹⁹

7^1/3 *7^1/2      7^√5 * 7^2         7^(1/3 + 1/2 + 2)          7^ 2  5/6

 

 

lub trochę inaczej:

 

  7 ^(1 + √5+5)                  7^(√5+6)                    7^(√5+6)              7^√5          7^6

--------------------------------- = ---------------------------=---------------------------= -----------  * --------------=

7^1/3 * 7^1/2 *7^(√5+2)       7^5/6 *7^(√5+2)        7^(√5 + 2  5/6)       7^√5           7^2  5/6

 

= 7^0 *  7^(6 - 2  5/6) = 1 * 7^(3  1/6) = 7^19/6 = ⁶√7¹⁹