Rational Exponents and Radicals

Write with radical. Assume that all variables represent positive real numbers.

$$\left(x^4y^4\right)^{\frac{1}{7}}$$  

Write with radical. Assume that all variables represent positive real numbers.

$$\left(5py^2\right)^{\frac{1}{3}}$$  

Write with radical. Assume that all variables represent positive real numbers.

$$\left(7m+n\right)^{\frac{8}{9}}$$  

Simplify by first converting to rational exponents. Assume that all variables represent positive real numbers.

$$\sqrt[4]{s^7}.\sqrt[3]{s^5}$$  

A rectangular coal bin has a length of $$\sqrt[]{45}$$   feet and a width of $$\sqrt[]{80}$$  feet. What is its perimeter?

Simplify by first converting to rational exponents. Assume that all variables represent positive real numbers.

$$\sqrt[3]{64x^6y^3}$$  

Simplify by first converting to rational exponents. Assume that all variables represent positive real numbers.

$$11\sqrt[3]{2}-4\sqrt[3]{128}$$  

Write with radicals. Assume that all variables represent positive real numbers.

$$\left(8x\right)^{\frac{4}{7}}+\left(3y\right)^{\frac{4}{5}}$$  

Simplify by first converting to rational exponents. Assume that all variables represent positive real numbers.

$$\frac{\sqrt[5]{w^6}}{\sqrt[7]{w^8}}$$  

Use the rules of exponents to simplify the expression. Write the answer with positive exponents. Assume that all variables represent positive real numbers

$$\left(\frac{x^2}{y^{-4}}\right)^{\frac{1}{2}}$$