Algebraic Skills

Roots and Rational Exponents

100

Evaluate 

64^1/2

8

200

Evaluate

 27^2/3

9

300

Simplify and write in radical form

x^3/4 x  x^1/2

4sqrt(x⁵)

400

Evaluate

16^-3/4

1/8

500

Simplify completely

(8x³/27y⁶)^-2/3

9y⁴/4x²

Simplifying Radicals

100

Simplify completely

sqrt 50

5sqrt(2)

200

Simplify completely

sqrt 72

6sqrt(2)

300

Simplify by rationalizing the denominator

6/sqrt(3)

2sqrt(3)

400

Simplify the expression

sqrt(20)+sqrt(45)

5sqrt(5)

500

Simplify by rationalizing the denominator

4/3-sqrt(5)

3+sqrt(5)

Factoring with Rational Coefficients

100

Factor out the fractional GCF

1/2x+5/2

1/2(x+5)

200

Factor completely

1/3x²-3

1/3(x-3)(x+3)

300

Factor completely

0.25x²-4

(0.5x-2)(0.5x+2)

or 

1/4(x-4)(x+4)

400

Factor completely 

1/2x²-2x-6

1/2(x-6)(x+2)

500

Factor completely

5/2x²-14/5x+4

2/5(x-5)(x-2)

Multiplying or Divide Rational Expressions

100

Simplify and state restrictions

5x²/y X y²/10x

xy/2

restrictions x cannot be 0, y cannot be 0

200

Simplify and state restrictions

x-5/x²-25

1/x+5

x cannot be +-5

300

Simplify and state restrictions

x²-9/5 X 10/x-3

2x+6 or 2(x+3)

X cannot be 3

400

Simplify and state restrictions

4x²/x+1 divided by 2x/x+1

2x

x cannot be -1,0

500

Simplify and state restrictions

x²-x-6/x²-4 X x+2/x-3

x+2/x-2

x cannot be 2,-2,3

Add or Subtract Rational Expressions

100

Simplify and state

x/x+2 + 2/x+2

1

x cannot be -2

200

Simplify and state restrictions

5/x + 2/3x

17/3x

x cannot be 0

300

Simplify and state restrictions

4/x-1 - 2/x

2x+2/x(x-1)

x cannot be 0,1

400

Simplify and state restrictions

3/x-2 - 1/x+3

2x+11/(x-2)(x+3)

x cannot be 2,-3

500

Simplify and state restrictions

2/x²-4 + 1/x-2

x+4/(x-2)(x+2)

x cannot be +-2