Insert the required factor in the parentheses.

$$x^{1 / 3}-5 x^{4 / 3}=x^{1 / 3}(\quad)$$

Solve the equation and check your solution. (If not possible, explain why.)

$$10-\dfrac{13}{x}=4+\dfrac{5}{x}$$

Rewrite the expression with positive exponents and simplify.

$$(z+2)^{-3}(z+2)^{-1}$$

Rewrite the expression with positive exponents and simplify.

$$\left(2 x^5\right)^0, \quad x \neq 0$$

Insert the required factor in the parentheses.

$$\dfrac{x^2}{4 / 9}+\dfrac{y^2}{7 / 8}=\dfrac{9 x^2}{()}+\dfrac{8 y^2}{(\quad)}$$

Solve the inequality and sketch the solution on the real number line. (Some inequalities have no solutions.)

$$3+\dfrac{2}{7} x>x-2$$

Solve the equation and check your solution. (If not possible, explain why.)

$$\dfrac{10 x+3}{5 x+6}=\dfrac{1}{2}$$

Describe the error.

$$\begin{aligned} \frac{x^2+25 x}{x^2-2 x-15}= & \frac{x\left(x^2+25\right)}{(x-5)(x+3)} \\ & =\frac{x(x+5)(x-5)}{(x-5)(x+3)}=\frac{x(x+5)}{x+3} \end{aligned}$$

Use inequality notation to describe the set.

All $y$ in the interval $[-6,0)$

Find the sum or difference and write the resulting polynomial in standard form. $-\left(5 x^{2}-1\right)+\left(-3 x^{2}+5\right)$

Rewrite the expression with positive exponents and simplify.

$$\left(2 x^2\right)^{-2}$$

Rewrite the expression with positive exponents and simplify.

$$(x+5)^0, x \neq-5$$

Solve the inequality and sketch the solution on the real number line. (Some inequalities have no solutions.)

$$\dfrac{3}{4} x-6 \leq x-7$$

Insert the required factor in the parentheses.

$$\dfrac{x^2}{1 / 12}-\dfrac{y^2}{2 / 3}=\dfrac{12 x^2}{()}-\dfrac{3 y^2}{()}$$