Question

(4,3*((5*5^(1/2)*5^(1/2))^(1/5)+0,7*5^(7/20))^(20/27)

Answer 1

Будет : 10.0199360705

Answer 2

Let's simplify the expression step by step:

1. First, we'll calculate the values inside the innermost parentheses:

   • $5^{1/2}$ is the square root of 5.
   • $5^{1/2} \cdot 5^{1/2}$ is the product of two square roots of 5, which equals 5 (since $\sqrt{a} \cdot \sqrt{b} = \sqrt{a \cdot b}$).
   • $5^{7/20}$ is the 20th root of 5 raised to the power of 7.

2. Next, we'll calculate the values inside the next set of parentheses:

   • $3 \cdot (5 \cdot 5^{1/2} \cdot 5^{1/2})^{1/5}$ can be simplified as follows:
     • $5 \cdot 5^{1/2} \cdot 5^{1/2}$ is 5 (as calculated above).
     • So, we have $3 \cdot (5)^{1/5}$.

3. Now, we'll calculate the values inside the outermost parentheses:

   • $(4 + 0.7 \cdot 5^{7/20})^{20/27}$:
     • $0.7 \cdot 5^{7/20}$ is a multiplication of a constant (0.7) and a number raised to a power (5^{7/20}).
     • $(4 + 0.7 \cdot 5^{7/20})$ is the sum of 4 and the above result.
     • Finally, $(4 + 0.7 \cdot 5^{7/20})^{20/27}$ is raising the sum to the power of 20/27.

Now, let's calculate each part:

1. $5^{1/2} \cdot 5^{1/2} = 5$
2. $3 \cdot (5)^{1/5} = 3 \cdot 1.903\ (rounded to 3 decimal places) \approx 5.709$
3. Calculate the result inside the outermost parentheses first:
   • $4 + 0.7 \cdot 5^{7/20} = 4 + 0.7 \cdot 1.903\ (rounded to 3 decimal places) \approx 5.332$
   • Now, calculate ((5.332)^{20/27}. This involves raising a number to a fractional power.

To calculate this, you can use a calculator or a math software:

$(5.332)^{20/27} \approx 4.647\ (rounded to 3 decimal places)$

So, the final result is approximately $4.647$.