Questions: 4. Есептендер: 1) √[6]2^6; 2) √[4](-3)^4; 3) -√[6]25^3; 4) √[3]125-√[4](-9)^4; 5) √[5]7^5; 6) √[3](-2)^3 7) (-3 √[3]3)^3; 8) √[5]32-√[6]27^2

Transcript text: 4. Есептендер: 1) $\sqrt[6]{2^{6}}$; 2) $\sqrt[4]{(-3)^{4}}$; 3) $-\sqrt[6]{25^{3}}$; 4) $\sqrt[3]{125}-\sqrt[4]{(-9)^{4}}$; 5) $\sqrt[5]{7^{5}}$; 6) $\sqrt[3]{(-2)^{3}}$ 7) $(-3 \sqrt[3]{3})^{3}$; 8) $\sqrt[5]{32}-\sqrt[6]{27^{2}}$

Solution

Solution Steps

Solution Approach

For the first question, $\sqrt[6]{2^{6}}$, we can simplify the expression by recognizing that the sixth root of $2^6$ is simply 2.
For the second question, $\sqrt[4]{(-3)^{4}}$, we can simplify the expression by recognizing that the fourth root of $(-3)^4$ is the absolute value of -3, which is 3.
For the third question, $-\sqrt[6]{25^{3}}$, we can simplify the expression by calculating the sixth root of $25^3$ and then taking the negative of that value.

Step 1: Calculate $ \sqrt[6]{2^{6}} $

We simplify the expression as follows: \[ \sqrt[6]{2^{6}} = 2^{\frac{6}{6}} = 2^{1} = 2.0 \]

Step 2: Calculate $ \sqrt[4]{(-3)^{4}} $

We simplify the expression as follows: \[ \sqrt[4]{(-3)^{4}} = | -3 |^{\frac{4}{4}} = 3^{1} = 3.0 \]

Step 3: Calculate $ -\sqrt[6]{25^{3}} $

We simplify the expression as follows: \[ -\sqrt[6]{25^{3}} = - (25^{3})^{\frac{1}{6}} = - 25^{\frac{3}{6}} = - 25^{\frac{1}{2}} = - \sqrt{25} = -5.0 \]