Question

Решите. 1. 1) (-7) ² 2) (-7)³ 3) (-1/2)⁴ 4) (-1/3)⁵ 2. 1) 4 7/12*(-1 3/11)-(-1 1/15)*(-45/64) 2) -81/88*(-6+(-1 13/15)*(-1 19/21)) 3. 3x-2|y-1| при x= -1, y= -4

Answer 1

Ответ:

Пошаговое объяснение:

1. 1) (-7) ²

=49

2) (-7)³ =-343

3) (-1/2)⁴

=1/16

4) (-1/3)⁵=-1/243

Answer 2

Let's solve each set of expressions step by step:

1. (-7)² = (-7) * (-7) = 49
2. (-7)³ = (-7) * (-7) * (-7) = -343
3. (-1/2)⁴ = (-1/2) * (-1/2) * (-1/2) * (-1/2) = 1/16
4. (-1/3)⁵ = (-1/3) * (-1/3) * (-1/3) * (-1/3) * (-1/3) = -1/243

1. 4 7/12 * (-1 3/11) - (-1 1/15) * (-45/64)

To simplify the first term, convert 4 7/12 to an improper fraction: 4 7/12 = (4 * 12 + 7) / 12 = 55/12

Now, multiply the fractions: (55/12) * (-1 3/11) = (55/12) * (-11/11 + 3/11) = (55/12) * (-8/11) = -440/132 = -55/16

To simplify the second term, convert -1 1/15 to an improper fraction: -1 1/15 = (-1 * 15 + 1) / 15 = -14/15

Now, multiply the fractions: (-14/15) * (-45/64) = 630/960 = 21/32

Now, subtract the second term from the first: -55/16 - 21/32 = -110/32 - 21/32 = (-110 - 21) / 32 = -131/32

2. -81/88 * (-6 + (-1 13/15) * (-1 19/21))

To simplify the second term, convert -1 13/15 to an improper fraction: -1 13/15 = (-1 * 15 + 13) / 15 = -2/15

Convert -1 19/21 to an improper fraction: -1 19/21 = (-1 * 21 + 19) / 21 = -2/21

Now, multiply the fractions: (-2/15) * (-2/21) = 4/315

Now, simplify the expression: -81/88 * (-6 + 4/315)

To add the fractions, find a common denominator, which is 315: -81/88 * (-1890/315 + 4/315) = -81/88 * (-1886/315)

Now, multiply the fractions: (-81/88) * (-1886/315) = 151746/27720 = 37/1352

To evaluate the expression 3x - 2|y - 1| when x = -1 and y = -4, plug in the values:

3(-1) - 2|(-4) - 1|

Perform the operations inside the absolute value first: 3(-1) - 2|-4 - 1| = -3 - 2|-5|

Now, calculate the absolute value: -3 - 2 * 5 = -3 - 10 = -13

So, the value of 3x - 2|y - 1| when x = -1 and y = -4 is -13.