oblicz:
1. 4⁻¹·(⅛)⁻²·64³=
2.
3.
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
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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