Question

Можно ли без корня решить эту задачу 4^0,3 (4 в степени 0,3)? И как?

Answer 1

Ответ:

Объяснение: (2^2)^3/10 = 2^3/5

Answer 2

Can the problem 4^0.3 + (4 raised to the power of 0.3) be solved without using a root?

To solve the problem 4^0.3 + (4 raised to the power of 0.3) without using a root, we can use the properties of exponentiation and logarithms.

Let's break down the problem step by step:

1. Express 4^0.3 as a logarithm: - We can rewrite 4^0.3 as 10^(0.3 * log10(4)). This is because 10 is a common base for logarithms and exponentiation. - Using the property of logarithms, we can rewrite 10^(0.3 * log10(4)) as 10^(log10(4^(0.3))). - Simplifying further, we get 4^(0.3).

2. Calculate 4^(0.3): - To calculate 4^(0.3) without using a root, we can use the property of exponentiation: a^(m/n) = (a^m)^(1/n). - Applying this property, we can rewrite 4^(0.3) as (4^3)^(1/10). - Simplifying further, we get 64^(1/10).

3. Calculate 64^(1/10): - To calculate 64^(1/10) without using a root, we can use the property of exponentiation: a^(1/n) = n√a. - Applying this property, we can rewrite 64^(1/10) as the 10th root of 64. - Calculating the 10th root of 64, we get the value of 1.58489319246.

4. Calculate the final result: - Now that we have the value of 4^(0.3) as 1.58489319246, we can substitute it back into the original expression: 4^0.3 + (4^0.3). - Plugging in the value, we get 1.58489319246 + 1.58489319246 = 3.16978638492.

Therefore, the solution to the problem 4^0.3 + (4 raised to the power of 0.3) without using a root is approximately 3.16978638492.