96. Вычислить: 1) 3/4 − (2/3)⁻¹; 2) (1/27 · 125⁻¹)^(−1/3); 3) 27^(2/3) + 9⁻¹; 4) (0,01)⁻² : 100^(−1/2); 5) (64/81)^(−1/2) · (8/5)⁻¹; 6) (2 10/27)^(−2/3) · (3/4)².

Question

Вопрос:

Accepted Answer

1) (2/3)⁻¹ = 3/2, поэтому 3/4 − 3/2 = 3/4 − 6/4 = −3/4.

2) 1/27 · 125⁻¹ = 1/(27 · 125) = 1/3375 = (1/15)³. Тогда ((1/15)³)^(−1/3) = (1/15)⁻¹ = 15.

3) 27^(2/3) + 9⁻¹ = (∛27)² + 1/9 = 9 + 1/9 = 82/9.

4) (0,01)⁻² : 100^(−1/2) = 10000 : 1/10 = 100000.

5) (64/81)^(−1/2) · (8/5)⁻¹ = 9/8 · 5/8 = 45/64.

6) 2 10/27 = 64/27 = (4/3)³. Следовательно, (64/27)^(−2/3) · (3/4)² = (4/3)⁻² · 9/16 = 9/16 · 9/16 = 81/256.

Ответ: 1) −3/4; 2) 15; 3) 82/9; 4) 100000; 5) 45/64; 6) 81/256.