Exponents and Scientific Notation

Rules

100

What do we do when we have exponents with the same bases being multiplied?

Keep the base and add the exponent

200

The first number in scientific notation has to be between __ and  __.

1, 10

300

What do we do  when we have exponents with the same bases being divided?

Keep the base subtract the exponents

400

Going from scientific to standard notation, if the exponent is NEGATIVE move the decimal __(1)__ and __(2)__ if the exponent is POSITIVE.

1. Left

2. Right 

500

What is the name of this exponent property: 

(x^m)ⁿ = x^mn

Power of a Power Property

Exponents

100

Write each expression using a positive exponent.

9^-4

1/9^4

200

Write the expression using a positive exponent.

(10)^-2

1/10^2

300

Simplify write using positive exponents.

3^-5 * 3^2

1/3^3

400

Simplify using positive exponents.

k^10 / k^4

k⁶

500

Simplify using Laws of Exponents: (6⁸)⁴

6³²

Operations in Sci. Notation

100

Multiply:  (3.1xx10^4)(5.8xx10^4) 

1.798 x 10⁹

200

Divide 

(3xx10^-2)/(12xx10^6)

2.5x 10^-9

300

Add:  (9.8xx10^-7)+(43.5xx10^-9) 

1.0235 x 10^-6

400

Subtract: 

(9.8xx10^7)-(3.21xx10^5)

9.7679 x 10⁷

500

(6xx10^4)^2

3.6 x 10⁹

Standard Notation to Scientific Notation

100

Express each number in scientific notation.

0.000561

5.61 x 10^-4

200

Express in scientific notation.

47,000

4.7 x 10⁴

300

Convert to scientific notation: 0.03452

3.452 xx 10^-2

400

Convert to scientific notation: 734,239

7.34239 xx 10^5

500

Convert to scientific notation: 8,000,000

8 xx 10^6

Simplify Exponents Challenge Problems

100

(3x^4)^4

3^4x^16 or 

81x^16

200

(x^3)(x^4)(x^-2)

x^5

300

x^7/x^10

1/x^3

400

(a^3)(a^9)(a^-7)

a^5

500

(2^0/(3x^2)^0)^12

1