Exponents and Scientific Notation

Negative and Zero

100

Anything to the zero power is this. 

1

200

True or False: 

Negative exponents make your answers negative.

False! 

Negative exponents are the reciprocal of positive exponents (looks like a fraction).

300

365⁰ + 2^{3 =} 

1 + 2³

1 + 8

9

400

3^-2 =

1/3²

OR

1/9?

500

(1/2)^-2 =

4

Multiplication Rule

100

When you multiply exponents with the same base, you do this to the exponents.

You add the exponents.

200

7^-5 x 7⁸ =

7³

300

9^-8 x 9⁴ =

9^-4

OR

1/9⁴

400

x⁵ * x^-4 * x⁷

x⁸

500

x^-4 * x^-4 * x^-5

x^-13

Power Rule

100

When you have a power to a power you do this.

What is multiply?

200

(4³)²=

(using positive exponents)

What is 4⁶?

300

(9^-4)^-2 =

(using positive exponents)

What is 9⁸?

400

(5² x 6^-4)^-2 =

(using positive exponents)

What is  6⁸ /5⁴ ? 

500

(9² x 8^-7 x 9³)²=

(using positive exponents)

What is 9¹⁰ / 8¹⁴ ?

Division Rule

100

When you are dividing two exponents with the same base, you do this with the exponents.

You subtract them.

200

5⁵/ 5² =

5³

300

6²/6⁸=

6^-6

OR

1/6⁶

400

(4² x 3³)/(4 x 3⁵)=

What is 4 / 3²?

500

(7² x 8⁵ x 9²) / (7³ x 9^-9)=

(using positive exponents)

What is   (8⁵ x 9¹¹) / 7 ?

Scientific Notation

100

True or false: This number is in scientific notation: 5.47 x 10²

What is true?

200

(2.5 x 10⁵) / (5 x 10³) in scientific notation.

What is 5 x 10¹?

300

(9.5 x 10³) x (2 x 10⁸) in scientific notation form.

What is 1.9 x 10¹²?

400

(2.53 x 10⁵) + (5 x 10³) in scientific notation.

What is 2.58 x 10⁵?

500

(9.5 x 10⁷) - (2.46 x 10⁵) in scientific notation form.

What is 9.4754 x 10⁷?