Unit 1 Jeopardy

Exponent Rules

100

Simplify.

b⁸ ÷ b¹⁰ = ?

b¹⁰ ÷ b⁸ = b^{10 - 8}

             = b^-2

Bonus 100 if you can write as a positive exponent.

200

Simplify

(-1)⁷⁴

(-1)⁷⁴

= +1 

There is a bracket and the exponent is an even number.

300

Simplify

(a³)(a²)(a^-1) =

(a3)(a2)(a^-1) = a^3+2-1

              = a⁴

400

Simplify

(x²y²)(2xy³)⁴

(x²y²)(2xy³)⁴

= (x²y²)(16x⁴y¹²)

= (16x⁶y¹⁴)

500

Simplify 

(-4ax² ÷ 2a⁴x³)^-2

Hint: write as a fraction!

https://imgur.com/a/JTXTzrR

(-4ax² ÷ 2a⁴x³)^-2

(2a⁴x³ ÷ -4ax²)²

4a⁸x⁶ ÷ 16a²x⁴

1/4a⁶x²

Terms and concepts

100

BONUS: What are the TWO things we have to do to change a positive exponent with negative exponent?

(100: first step)
(100: second step)
(100: name of word beginning with "r" meaning to flip?) 

- change the sign

- flip / swap numerator with denominator 

> (this is called "reciprocate")

200

Write the expanded form of 3⁴

3⁴ = 3 x 3 x 3 x 3

300

What type of polynomial is this?

3x² + 4x + 5y - 2x 

3x² + 4x + 5y - 2x can be simplified into:

3x² + 2x + 5y 

So it is not a four-term polynomial, but a trinomial

400

What is the degree of this term?

5x³y²z

3+2+1(on the z) = 6

500

What is the degree of this polynomial?

5a²b³ + ab⁵ - 2a²b²

6 

(the term with the degree is ab⁵ which has a sum of 1+5 for its exponents)

Polynomials

100

Simplify

2a + 5a - 3a 

4a

Bonus (100): what kind of polynomial is this?

200

Simplify

(2a + 3b) - (2a - 4b)

(2a + 3b) - (2a - 4b)
= 2a + 3b - 2a + 4b

= 7b

300

Simplify

2a(2a + 3)

4a² + 6a

400

(6x2 - 2x) ÷ (-2x)

-3x + 1

500

Rolly plans to paint a picture frame that has a length of (4x + 2) and a width of (3x). If the area inside the frame can be expressed as 6x + 6, what is the expression for the area that needs to be painted?

Area of entire frame including photo:
A = L x W
= (4x + 2)(3x)
= 6x² + 6x

Area of frame:
Total area - photo
(6x² + 6x) - (6x + 6)
6x² + 6x - 6x - 6
6x² - 6

ETC.

100

25 - (25a - 25b)⁰

(anything to the exponent 0 is 1)

25 - 1 = 24

200

A rectangle has the side lengths x+1 and a width of 2x+2. What is the expression for perimeter?

Perimeter = side 1 + side 2 + side 3 + side 4

= (x+1) + (x + 1) + (2x+2) + (2x+2)

= 6x + 6

300

(100 points each)

Fill in the following blanks:

Product Rule: ___ exponents
Quotient Rule: ____ exponents
Power Rule: ______ exponents

Product Rule: add exponents
Quotient Rule: subtract exponents
Power Rule: multiply exponents

400

A square has a side length of x - 1. What is the SIMPLIFIED expression for the area?

A = L x W
= (x - 1)(x - 1)
= (x² - x - x + 1)
= (x² - 2x + 1)

500

A triangle has  a base of (x + 1) and a height of (2x), what is the expression for the area of the triangle?

A = (base x height) / 2
= (x + 1)(2x) / 2
= (2x² + 2x) / 2
= (x² + x)