Question

0,34^3 : 0,17^3 - 0,5^6 * 2^6 = 36^5/(2^10 * 3^11) =

Answer 1

Ответ:

Применяем свойства степеней:

    $\bf \dfrac{a^{k}}{b^{k}}=\Big(\dfrac{a}{b}\Big)^{k}\ \ ,\ \ a^{k}\cdt b^{k}=(ab)^{k}\ \ ,\ \ (a^{k})^{n}=a^{k\cdot n}\ \ ,\ \ \dfrac{a^{k}}{a^{n}}=a^{k-n}$   .

$0,34^3:0,17^3-0,5^6\cdot 2^6=\Big(\dfrac{0,34}{0,17}\Big)^3-(0,5\cdot 2)^6=2^3-1^6=8-1=\bf 7$  

$\dfrac{36^5}{2^{10}\cdot 3^{11}}=\dfrac{(6^2)^5}{2^{10}\cdot 3^{11}}=\dfrac{(2^2\cdot 3^2)^5}{2^{10}\cdot 3^{11}}=\dfrac{2^{10}\cdot 3^{10}}{2^{10}\cdot 3^{11}}\bf =\dfrac{1}{3}$

Answer 2

Let's break down the expression step by step:

0,34^3 / 0,17^3 - 0,5^6 * 2^6

First, we'll calculate the exponentiation:

0,34^3 = 0.34 * 0.34 * 0.34 ≈ 0.039304 0,17^3 = 0.17 * 0.17 * 0.17 ≈ 0.004913 0,5^6 = 0.5 * 0.5 * 0.5 * 0.5 * 0.5 * 0.5 = 0.015625 2^6 = 2 * 2 * 2 * 2 * 2 * 2 = 64

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

0.039304 / 0.004913 - 0.015625 * 64

Next, we'll perform the multiplication and division:

0.039304 / 0.004913 - 1 * 64

0.039304 / 0.004913 - 64

Now, we'll calculate the division:

(0.039304 / 0.004913) - 64 ≈ 8 - 64

Finally, we'll perform the subtraction:

8 - 64 = -56

So, the value of the expression 0,34^3 : 0,17^3 - 0,5^6 * 2^6 is approximately -56.

Moving on to the next part:

36^5 / (2^10 * 3^11)

Let's calculate the exponentiation:

36^5 = 36 * 36 * 36 * 36 * 36 = 60466176 2^10 = 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 = 1024 3^11 = 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 ≈ 177147

Now, we substitute these values back into the expression:

60466176 / (1024 * 177147)

Next, we perform the multiplication:

60466176 / 180633088

Finally, we calculate the division:

0.335 ≈ 0.33499879922 (rounded to 3 decimal places)

So, the value of the expression 36^5 / (2^10 * 3^11) is approximately 0.335 (rounded to 3 decimal places).

Therefore, the final expression evaluates to approximately 0.335.