Question

1) (4/3)^2×(3/4)3÷(-2/3)^-3×(-1/2)^-7= 2) ((2^3/5)^-1-3×(-2)^-3+(7/8)^0)^1= 3) (-2,2)^5×(2 3/11)^4=

Answer 1

1)2 1/3 : 2 2/3 * 1 3/5 = 7/3 : 8/3 * 8/5 = 1,47/3 : 8/3 = 7/3 * 3/8 = 7/87/8*8/5 = 7/5 = 1,4
2)2 1/4 * 12/13 : 3 3/8 = 9/4 * 12/13 : 27/8 = 8/139/4*12/13=27/1327/13*8/27=8/13
3) 3 2/3 : 7 1/3 * 2/5 = 11/3 : 22/3 * 2/5 = 0,211/3*3/22=1/21/2 * 2/5 = 1/5 = 0,2
4)1 1/9 * 2 1/5 : 7 1/3 = 10/9 * 11/5 : 22/3 = 1/310/9*11/5=22/922/9*3/22= 1/3

Answer 2

1) Let's break down the expression step by step:

First, let's simplify the exponents: (4/3)^2 = (16/9) (-2/3)^-3 = (-3/2)^3 = (-27/8) (-1/2)^-7 = (-2/1)^7 = (-128/1)

Next, let's simplify the fractions: (3/4)3 = (3/4) * (3/4) * (3/4) = (27/64)

Now, let's substitute the simplified values back into the expression: (16/9) * (27/64) ÷ (-27/8) * (-128/1)

To divide fractions, we need to multiply by the reciprocal of the second fraction: (16/9) * (27/64) * (-8/27) * (-1/128)

Now, let's simplify the fractions and multiply them together: (16 * 27 * -8 * -1) / (9 * 64 * 27 * 128) (-27648) / (186624) -27648 / 186624 = -0.148

Therefore, the answer to the first part of the expression is -0.148.

2) Let's break down the expression step by step:

First, let's simplify the exponents: (2^3/5)^-1 = (5/2)^-1 = (2/5) (-2)^-3 = -2^-3 = -1/8 (7/8)^0 = 1

Next, let's substitute the simplified values back into the expression: ((2/5) - 3 * (-1/8) + 1)^1

Now, let's simplify the expression inside the parentheses: (2/5) + 3/8 + 1 (16/40) + (15/40) + (40/40) (16 + 15 + 40) / 40 71 / 40

Therefore, the answer to the second part of the expression is 71/40.

3) Let's simplify the expression step by step:

(-2.2)^5 = (-2.2) * (-2.2) * (-2.2) * (-2.2) * (-2.2) = 10.64896

(2 + 3/11)^4 = (2 + 3/11) * (2 + 3/11) * (2 + 3/11) * (2 + 3/11) = (22/11 + 3/11) * (22/11 + 3/11) * (22/11 + 3/11) * (22/11 + 3/11) = (25/11) * (25/11) * (25/11) * (25/11) = (625/121)

Now, let's substitute the simplified values back into the expression: 10.64896 * (625/121)

To multiply a decimal by a fraction, we convert the decimal to a fraction first: 10.64896 = 1064896/100000

Now, let's multiply the fractions: (1064896/100000) * (625/121)

To multiply fractions, we multiply the numerators together and the denominators together: (1064896 * 625) / (100000 * 121)

Now, let's simplify the expression: 664310000 / 12100000 55

Therefore, the answer to the third part of the expression is 55.

Overall, the simplified expression is: -0.148 + 71/40 + 55