Laws of Exponents

Exponents

1

Identify the base: 3^2

the base is 3

1

Identify the exponent 1^6

the exponent is 6.

2

Write using exponents: (3 x 3 x 3)

 3³

2

Write using exponents: h x h x h x h x h

h⁵

3

Write in expanded form: 9^6

9⁶ = 9 x 9 x 9 x 9 x 9 x 9

Product of Powers

1

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

add the exponent

1

Simplify: 5² x 5⁶

 5⁸

2

Simplify: 2x² times 4x³

 8x⁵

2

Simplify: (8x³)(-3x⁹)

 -24x¹²

3

Make up your own product of powers question.

answer it correctly!

Quotient of Powers

1

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

What is subtract

1

Simplify:  2⁵/2²

 2³

2

Simplify: w³/w⁸

w^-5 or 1/w^-5

2

18a^7/6a^3

What is 3a^4

3

Simplify: 12x^2/6x^3

What is 2x^-1

Power of Powers

1

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

What is multiply

1

Simplify: (z^11)^5

What is z^55

2

Simplify: (4^3)^2

What is 4^6

2

Simplify: (14y)^4

What is 38416y^4

3

Simplify: (x^2y^6)3

What is x^6y^18

Negative and Zero Exponents

1

Any number raised to the zero power is

What is 1

1

2^0

What is 1

2

To write a negative fraction using positive exponents, you must make a

What is fraction.

2

Write using a positive exponent w^-5

What is 1/w^5

3

Write x^-1 using positive exponents.

What is 1/x^1