Algebra 1, 8th grade

Properties of Exponents

100

Solve:

x^{4  .}  x⁵

X⁹  

^{If bases are the SAME, just add the exponents when you multiply} 

200

4^{2  .}   6²

24²  = 576

If exponents are the SAME... keep the exponents the same, and MULTIPLY your bases

300

Solve:    x⁰

Answer: 1

ANY number or value raised to the "zeroeth" power will be 1.

400

Solve: (x³)⁴

Answer: x¹²

When you see parethesis in an exponential expression, MULTIPLY the exponents.

500

Solve: x⁷   divided by  x³

Answer: x⁴

When dividing exponents, subtract them(left from right or if a fraction, top to bottom

Negative exponents

100

Change to be positive: x^-2

Answer: 1/x²

NEVER leave an exponent as a negative. make it into a fraction to make it positive. 

200

Solve:  (4/3)^-2

1. Flip the fraction to make it positive: 3/4

2. Distribute the exponent to top and bottom: 4²/3²

3. Solve, and simplify your fraction if you can.  16/9

300

Solve: (4x^-5)²

1. Distribute the exponent on the outside of the parenthesis:  4² x^-10

2. Get rid of the negative exponent by making it a fraction: 4² / x¹⁰

3. Solve your exponents if you can:  16/x¹⁰

400

Solve:  y⁵   /   y^-3

Answer: y⁸       

5 - (-3) = 5 + 3

500

Solve:  (-3)²

Answer: 9

(-3) (-3) = 9

Algebra with perimeter and area

100

Solve the area of this rectange:

Length: 5x

Width: 2x

Answer: 10x²

200

Write an espression for the area of this rectangle. Write in the simplest form.

Width:  5x 

Length:  5x - 4

Answer: 25x² - 20x

300

Write an algebraic expression for the perimeter of this rectangle:

Width: 5x - 4 

Length: 5x

Answer: 20x - 8

400

Write an expression for the formula for perimeter of this rectangle:

Width: 10x + 6

Length: x - 1

Answer: 10x + 6

500

A square has sides that are represented by: 3x³

Write an expression for the area.

Answer: (3x³)² = 9x⁶

Exponential Expressions

100

Re-write this expression with the values given for "s" and "t". DO NOT SOLVE.

s -t - 10                                 s= -8  ,   t = 3/4

Answer:  -8²  (3/4)  -10

200

Re-write this expression. Do NOT solve.

(a + b)⁵  /  a - 2b²     when a = 6, b = -8

Answer: (6 + - 8)⁵ / 6 -2(-8)²

300

Solve: 5c² - d² +3 / 2c - 4d

Answer: 4/-7

 number 8, page 9???

400

Solve:  4p²  +  7p³

Answer:  -20   (see page 9 of homework packet for details. We tried this twice.)

500

Combine like terms: 

k² -9k +23 + 2(k²+k) + 2k² -17

Answer: 5k² -7k +6

Mixed Bag

100

Solve: -3²

Answer: - 9

- (3) (3) = -9

200

Solve:  5x³          when     x=4

Answer: 5 ^. 4³

5  ^. 64 = 320

300

Does (a + b)²  = a² +b^{2   ???}

Answer: No!!!

(a +b)² =  (a +b) (a +b) which is actually written as: " a² + ab + ab + b² "

400

Solve:  -q²  -r²  + 3s    when     s= - 20, r = -6, s= -20

Answer: -15

500

 Factor:  8y - 12y 

Answer: 4y (2-3)