Question

81^-0,75+(1/125)^-1/3-(1/32)-3/5

Answer 1

Ответ:разберём по частям

1)81^-3/4=корень 4йстепени (81^-3)=1/81^3=1/3^3=1/27

2)5

3)1/27+5-1/32-3/5=5+-839/4320

Пошаговое объяснение:

Answer 2

Возможно, Вы забыли указать значок возведения в степень -3/5 в последнем слагаемом. Если это так, то:

81^-0,75 +( 1/125)^-1/3 - (1/32)-3/5 =
= 81^(3/4) + (1/125)^(-1/3) - (1/32)^(-3/5) =
= (3^4)^(3/4) + (5^(-3))^(-1/3) - (2^(-5))^(-3/5) =
= 3^(4•3/4) + 5^((-3)•(-1/3)) - 2^((-5)•(-3/5)) =
= 3^3 + 5^1 - 2^3 =
= 27 + 5 - 8 = 24

Ответ: 24.

Answer 3

Let's break down the expression step by step:

1. 81^-0.75: This means raising 81 to the power of -0.75. To simplify this, we can rewrite 81 as 3^4 since 3^4 = 81. (3^4)^(-0.75) = 3^(-3) So, 81^-0.75 is equal to 3^(-3).

2. (1/125)^(-1/3): This means raising 1/125 to the power of -1/3. We can rewrite 1/125 as 5^(-3) since 5^(-3) = 1/125. (5^(-3))^(-1/3) = 5^(1) So, (1/125)^(-1/3) is equal to 5^(1).

3. (1/32)^(-3/5): This means raising 1/32 to the power of -3/5. We can rewrite 1/32 as 2^(-5) since 2^(-5) = 1/32. (2^(-5))^(-3/5) = 2^(3) So, (1/32)^(-3/5) is equal to 2^(3).

Now, let's calculate the values:

1. 81^-0.75 = 3^(-3) = 1/(3^3) = 1/27.

2. (1/125)^(-1/3) = 5^(1) = 5.

3. (1/32)^(-3/5) = 2^(3) = 8.

Now, let's substitute these values back into the original expression:

1/27 + 5 - 8/5

To simplify this further, let's convert 1/27 to a common denominator with 8/5:

1/27 = (1/27) * (5/5) = 5/135

Now, let's substitute the values:

5/135 + 5 - 8/5

To combine the fractions, we need a common denominator. The least common multiple of 135 and 5 is 135, so:

(5/135) + (675/135) - (216/135)

Now, we can add the fractions:

(5 + 675 - 216)/135 = 464/135

So, the simplified value of the expression 81^-0.75 + (1/125)^-1/3 - (1/32)^-3/5 is 464/135.