Question

Тема:степени и корни. Помогите разобраться с данным примером (3√(2^2*√2))в степени 6/5. Распишите пожалуйста с пояснениями, а то я запутался уже.

Answer 1

 

$(3\sqrt{2^2\cdot\sqrt2})^\frac{6}{5}=3^\frac{6}{5}((2^2\cdot2^\frac{1}{2})^\frac{1}{2})^\frac{6}{5}=3^\frac{6}{5}(2^{2+\frac{1}{2}})^{\frac{1}{2}\cdot\frac{6}{5}}=3^\frac{6}{5}\cdot2^{\frac{5}{2}\cdot\frac{3}{5}}= \\ =3^\frac{6}{5}\cdot2^\frac{3}{2}$

Answer 2

Understanding the Expression (3√(2^2*√2))^(6/5)

To understand the expression (3√(2^2*√2))^(6/5), let's break it down step by step.

1. Simplify the Inside of the Root: - First, let's simplify the inside of the cube root. We have 2^2 * √2 inside the cube root.

- The expression 2^2 simplifies to 4, so we have 4 * √2 inside the cube root.

2. Evaluate the Cube Root: - Now, let's evaluate the cube root of 4 * √2.

- The cube root of 4 is 1.5874, and the cube root of √2 is 1.1892.

- Therefore, the cube root of 4 * √2 is approximately 1.5874 * 1.1892, which equals approximately 1.8874.

3. Raise the Result to the Power of 6/5: - Finally, we need to raise the result of the cube root to the power of 6/5.

- To do this, we raise 1.8874 to the power of 6/5.

- The result of raising 1.8874 to the power of 6/5 is approximately 2.0805.

So, the value of the expression (3√(2^2*√2))^(6/5) is approximately 2.0805.

I hope this helps clarify the expression for you! If you have any further questions or need additional assistance, feel free to ask.