91Ó°ÊÓ

In Exercises \(109-110\), evaluate each expression. $$\sqrt[3]{\sqrt[4]{16}+\sqrt{625}}$$

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. In one short sentence, five words or less, explain what $$\frac{\frac{1}{x}+\frac{1}{x^{2}}+\frac{1}{x^{3}}}{\frac{1}{x^{4}}+\frac{1}{x^{5}}+\frac{1}{x^{6}}}$$ does to each number \(x\).

$$\text { Factor completely.}$$ $$x^{4}-5 x^{2} y^{2}+4 y^{4}$$

Simplify each exponential expression. Assume that variables represent nonzero real numbers. $$\left(3 x^{-4} y z^{-7}\right)(3 x)^{-3}$$

$$\text { Factor completely.}$$ $$x^{4}-10 x^{2} y^{2}+9 y^{4}$$

In Exercises \(109-110\), evaluate each expression. $$\sqrt[3]{\sqrt{\sqrt{169}+\sqrt{9}}+\sqrt{\sqrt[3]{1000}}+\sqrt[3]{216}}$$

Will help you prepare for the material covered in the first section of the next chapter. If \(y=4-x^{2},\) find the value of \(y\) that corresponds to values of \(x\) for each integer starting with \(-3\) and ending with 3

Use the order of operations to simplify each expression. $$8^{2}-16 \div 2^{2} \cdot 4-3$$

In Exercises \(111-114\), simplify each expression. Assume that all variables represent positive numbers. $$\left(49 x^{-2} y^{4}\right)^{-\frac{1}{2}}\left(x y^{\frac{1}{2}}\right)$$

In Exercises 111–113, perform the indicated operations. $$[(7 x+5)+4 y][(7 x+5)-4 y]$$