Laws of Exponents

Exponents

100

Identify the base: 3²

What is 3

200

Identify the exponent 1⁶

What is 6.

300

Evaluate (-3)³

What is -27

400

Write in standard form: -4² 

What is -16

500

Write the missing exponent for x: g³/g^x = g^-5

What is x=8

Product of Powers

100

You do this to the exponents to multiply powers with the same base.

What is add.

200

Simplify: (-4)² * (-4)⁶

What is (-4)⁸

300

Simplify: 2x² * 4x³

What is 8x⁵

400

Simplify: (8a⁴x³)(-3ax⁹)

What is -24a⁵x¹²

500

Simplify using only positive exponents: c⁴d⁴f³ * c^-6d³f^-8

What is d⁷/c²f⁵

Quotient of Powers

100

You do this to the exponents when dividing powers with the same base.

What is subtract

200

Simplify: 2⁵/2²

What is 2³

300

Simplify using only positive exponents: w³/w⁸

What is 1/w⁵

400

Simplify: 18a⁷/6a³

What is 3a⁴

500

Simplify: 4x²y³/12x³y

What is y²/3x

Power of Powers

100

You do this to the exponents when finding the power to a power.

What is multiply

200

Simplify: (z¹¹)⁵

What is z⁵⁵

300

Simplify using standard form: (4x³)²

What is 16x⁶

400

Simplify using exponents: (4²y⁴z⁸)⁴ 

What is 4⁸y¹⁶z³²

500

Simplify using standard form: (x²y⁶)³ * (5xy³)² 

What is 25x⁸y²⁴

Negative and Zero Exponents

100

Any number raised to the zero power is

What is 1

200

Simplify using standard form: 

(32xy^-4)⁰ * 8^-2

What is 1/64

300

Simplify using standard form:  

8²m^-2x

64x/m²

400

Simplify using only positive exponents: (7x²y/49)^-1

What is 7/x²y

500

Simplify using standard form:  12²/6²

What is 4