0. Review of Algebra

Simplify each expression. Write answers without negative exponents. Assume all vari-ables represent positive real numbers. See Examples 8 and 9. (z^1/3z^-2/3z^1/6)/(z^-1/6)^3

In Exercises 103–110, insert either <, >, or = in the shaded area to make a true statement. 30/40−3/4 □ 14/15⋅15/14

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

Evaluate each expression for p=-4, q=8, and r=-10. q/2-r/3 / 3p/4+q/8

In Exercises 101–108, simplify by reducing the index of the radical. ⁹√x^6 y^3

Evaluate each expression for p=-4, q=8, and r=-10. -(p+2)²-3r / 2-q

Calculate each value mentally. (0.25^3)(400^3)

Perform the indicated operations. Assume all variables represent positive real numbers. ∛64xy² + ∛27x⁴y⁵

Calculate each value mentally. (24^2)(0.5^2)

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^−2y^4)^−1/2(xy^1/2)

Perform the indicated operations. Assume all variables represent positive real numbers. ∜81x⁶y³ - ∜16x¹⁰y³

Calculate each value mentally. 15^4/5^4

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