Step 1: Use the power of a power rule: (a^m)^n = a^(m*n). Step 2: Here (a^2)^3 = a^(2*3) = a^6.

Step 1: | -4 | = 4. Step 2: -| -4 | = -4. Step 3: -4 + 3 = -1.

Step 1: Normalize to the same number of decimal places: 8.90 and 8.11. Step 2: Compare digit by digit: at the tenths place both are 8. At the hundredths place 9 > 1. Step 3: Therefore 8.90 > 8.11.

Step 1: A rational number can be written as a ratio a/b of integers. Step 2: 0.333... repeating equals 1/3, which is rational. Step 3: sqrt(2), sqrt(5), and pi are irrational.

Step 1: On the number line, negative numbers are left of 0 and positive numbers are right of 0. Step 2: Therefore -3 is left of 0 and 4 is right of 0, giving -3 < 0 < 4.

Step 1: By the definition of absolute value, |x| = 7 means the distance of x from 0 is 7. Step 2: There are two solutions: x = 7 and x = -7.

Step 1: Factor inside the root: sqrt(50) = sqrt(25*2). Step 2: sqrt(25) = 5. Step 3: Therefore sqrt(50) = 5*sqrt(2) in simplest radical form.

Step 1: 81 is a perfect square: 81 = 9*9. Step 2: Therefore sqrt(81) = 9.

Step 1: Division by a fraction equals multiplication by its reciprocal: (5/6)*(3/1). Step 2: Multiply: 15/6. Step 3: Simplify 15/6 by dividing by 3: 5/2.

Step 1: Multiply numerators and denominators: (3*10)/(5*9) = 30/45. Step 2: Simplify 30/45 by dividing by 15: 2/3.