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. 100^3/2

Simplify each expression. Write answers without negative exponents. Assume all vari-ables represent positive real numbers. See Examples 8 and 9. -81^3/4

Simplify each expression. Write answers without negative exponents. Assume all vari-ables represent positive real numbers. See Examples 8 and 9. (27/64)^-4/3

Simplify each expression. Write answers without negative exponents. Assume all vari-ables represent positive real numbers. See Examples 8 and 9. (x^2/3)²/(x²)^7/3

Simplify each expression. Write answers without negative exponents. Assume all vari-ables represent positive real numbers. See Examples 8 and 9. (p³)^1/4/(p^5/4)²

Simplify each expression. Write answers without negative exponents. Assume all vari-ables represent positive real numbers. See Examples 8 and 9. (p^1/5p^7/10p^1/2)/(p³)^-1/5

Calculate each value mentally. (0.1^3/2)(90^3/2)

Simplify each rational expression. Assume all variable expressions represent positive real numbers. (Hint: Use factoring and divide out any common factors as a first step.) [2(2x-3)^1/3 - (x-1)(2x-3)^-2/3] / [(2x-2)^-2/3]

Solve: 5x^3/4- 15 = 0.

Solve for x: x^(5/6) + x^(2/3) - 2x^(1/2) = 0

In Exercises 91–100, find all values of x satisfying the given conditions. $y = (x - 5)^{\frac{3}{2}} \quad \text{and} \quad y = 125$

Exercises 177–179 will help you prepare for the material covered in the next section. If $-8$ is substituted for x in the equation $5x^{\frac{2}{3}}+11x^{\frac{1}{3}}+2=0$, is the resulting statement true or false?

Solve each equation. See Example 7. x^3/2 = 125

Solve each equation. See Example 7. x^5/4 = 32

Solve each equation for the specified variable. (Assume all denominators are nonzero.) x^2/3+y^2/3=a^2/3, for y