0. Review of Algebra

Evaluate each expression for $p=-4$, $q=8$, and $r=-10$. $\frac{\frac{q}{2}-\frac{r}{3}}{\frac{3p}{4}+\frac{q}{8}}$

Simplify by reducing the index of the radical. $\sqrt[9]{x^6{y}^3}$

Evaluate each expression for $p=-4$, $q=8$, and $r=-10$. $\frac{-(p + 2)^2 - 3r}{2 - q}$

Calculate each value mentally. (0.25³)(400³)

Perform the indicated operations. Assume all variables represent positive real numbers. $\sqrt[3]{64xy^2} + \sqrt[3]{27x^4y^5}$

Calculate each value mentally. (24²)(0.5²)

In Exercises 107–114, simplify each exponential expression. Assume that variables represent nonzero real numbers. (3x−4 y z−7)(3x)−3

In Exercises 111–114, simplify each expression. Assume that all variables represent positive numbers. (49x−2y⁴)^−1/2(xy^1/2)

Perform the indicated operations. Assume all variables represent positive real numbers. $\sqrt[4]{81x^6y^3} - \sqrt[4]{16x^{10}y^3}$

Calculate each value mentally. 15⁴/5⁴

Calculate each value mentally. (0.2^2/3)(40^2/3)

In Exercises 111–114, simplify each expression. Assume that all variables represent positive numbers. (x^−5/4y^1/3x^−3/4)⁻⁶

Perform the indicated operations. Assume all variables represent positive real numbers. 5√6 + 2√10

In Exercises 107–114, simplify each exponential expression. Assume that variables represent nonzero real numbers. (2^−1x^−3y^−1)^−2(2x^−6y^4)^−2(9x^3y^−3)^0/(2x^−4y^−6)^2