To make the given statement valid, use either <, >, = in the shaded area.

|8²∙(-1)³/4 + 10| □ |5³/(3² + 4²)|

By using rules of exponents, identify if the given statement is true or false. If the statement is false, modify the right side of the equation to make the equation correct.

(x^1/9)(x^5/9) = x^5/81

Given the expression $\sqrt{4m^4}\cdot\sqrt{8m}$ , where $m$ is a nonnegative real number, simplify it using the product rule.

Given the expression $\frac{\sqrt{200z^8}}{\sqrt{5z}}$ , where $z$ is a nonnegative real number, simplify it using the quotient rule.

Rationalize the denominator of the radical expression.

$\frac{23}{23+\sqrt{19}}$

Rationalize the denominator of the following expression.

$\frac{3+\sqrt5}{2\sqrt{17}+5\sqrt2}$

Rationalize the denominator of the following expression.

$\frac{8\sqrt{a}}{11\sqrt{2a}+\sqrt{b}}$

Perform the following operation and evaluate it by applying radical rules and simplification techniques. 

√17 • √68

Consider the given expression and simplify it:

-64^5/6

Solve the given expression, and the answer should be written without negative exponents. (Let all the variables shown belong to ℝ⁺): (a⁵)^1/3/(a^2/3)⁴