Exponent Laws and Algebra

Vocabulary

100

A monomial only has one of these.

What is a term?

200

This refers to the number at the front of a term.

What is a coefficient?

300

-4x²y³ and 2x²y³ are examples of these.

What are like terms?

400

a^b is called this.

What is a power?

500

The act of multiplying each term in a bracket by the term on the outside is called the _______ property.

What is distributive?

Positive Exponent Laws

100

Simplify.

(3x⁵)²

9x¹⁰

200

Simplify.

(-2x⁷y³)(5x²y⁸)

10x⁹y¹¹

300

Simplify.

9x⁶/-6x²

-3x⁴/2

400

Simplify.

(2x³y²)³(3xy⁴)

24x¹⁰y¹⁰

500

Simplify.

(8x⁶y⁸)(6x⁸y⁵)/(-4x⁶y³)²

3x²y⁷

Simplifying Like Terms

100

Simplify and write in proper order.

2a+3b-7a+4a+b

-a+4b

200

Simplify and write in proper order.

(3a+2b-4c)-(7a+2b-c)

-4a-3c

300

Simplify and write in proper order.

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

4a+15b-17c

400

Simplify and write in proper order.

x²(3x³-2x²+x)+2x³(5-x²+4x)

x⁵+6x⁴+11x³

500

Simplify and write in proper order.

-3x²y⁴(5xy-2x⁴y⁷+2)-xy³(4xy+3x⁵y⁸-2x²y²)

3x⁶y¹¹-13x³y⁵-10x²y⁴

Negative Exponent Laws

100

Simplify. Express with positive exponents.

(a³b^-5)^-2

b¹⁰/a⁶

200

Simplify. Express with positive exponents.

(-9x⁶y^-3)(-2x^-4y^-5)

18x²/y⁸

300

Simplify. Express with positive exponents.

(18x²y³) / (6x³y^-4)

3y⁷/x

400

Simplify. Express with positive exponents.

(x⁵y³)^-3(4x^-2y⁷)

4/x¹⁷y²

500

Simplify. Express with positive exponents.

(3x²y^-6/2x⁸y)^-2

4x¹²y¹⁴/9

Questions with Fractions

100

Simplify and write in proper order.

1/2 a + 3/4 b - 2/3 a + 1/3 b

-1/6 a + 13/12 b

200

-3a+ 2/5 b - (5/4 a - 2/3 b)

-17/4 a + 16/15 b

300

Expand and simplify. 

3/4 x²(4x - 3x² + 1/2) + 2x(6/5 x³ - x² - 1/3 x)

3/20 x⁴ + x³ - 7/24 x²

400

Find the missing value.

-2/5 x² ( ? x⁶) = -3/2 x⁸

? = 15/4

500

(x^?)(x^3/4) = x^1/4

? = -1/2