91Ó°ÊÓ

Find all numbers that must be excluded from the domain of each rational expression. $$ \frac{x+7}{x^{2}-49} $$

Use the product rule to simplify the expressions in Exercises \(7-16 .\) In Exercises \(11-16,\) assume that variables represent nonnegative real numbers. $$\sqrt{6 x} \cdot \sqrt{3 x^{2}}$$

Use the quotient rule to simplify the expressions in Exercises \(17-26 .\) Assume that \(x>0\) $$\sqrt{\frac{121}{9}}$$

In Exercises \(27-38,\) add or subtract terms whenever possible. $$4 \sqrt{13 x}-6 \sqrt{13 x}$$

express the distance between the given numbers using absolute value. Then find the distance by evaluating the absolute value expression. 4 and 15

express the distance between the given numbers using absolute value. Then find the distance by evaluating the absolute value expression. \(-19\) and \(-4\)

express the distance between the given numbers using absolute value. Then find the distance by evaluating the absolute value expression. \(-26\) and \(-3\)

Simplify each exponential expression $$ \frac{8 x^{20}}{2 x^{4}} $$

Simplify each exponential expression $$ \left(\frac{3 a^{-5} b^{2}}{12 a^{3} b^{-4}}\right)^{0} $$

Doctors use the rational expression $$\frac{D A}{A+12}$$ to determine the dosage of a drug prescribed for children. In this expression, \(A=\) child's age, and \(D=\) adult dosage. What is the difference in the child's dosage for a 7-year-old child and a 3 -year-old child? Express the answer as a single rational expression in terms of \(D .\) Then describe what your answer means in terms of the variables in the rational expression.