8th Grade Exponents and Scientific Notation

Powers and Negative Exponents

100

Write the expression using exponents.

x*x*x

x^3

200

Evaluate each expression.

(-4)^3

-64

300

Write each exponent using a positive power.

(-4)^-3

1/((-4)^3)

400

simplify and express your answer using a positive exponent

x³ * x^-5 * (x⁴)^-2

x^-10 = 1/x¹⁰

500

Michigan State has 2 x 10³ students. Michigan University has 20,000 students. How many times more students does Michigan U have compared to Michigan State?

10 times more students

Multiplying and Dividing Exponents

100

Find each product. Express using positive exponents.

m^3*m^6

m^9

200

Find each quotient. Express using positive exponents.

k^10/k^4

k^6

300

Find each product. Express using positive exponents.

x^8*x*x*x^2

x^12

400

Find each product. Express using positive exponents.

(a^-3)/(a^4)

1/a¹²

500

Find each quotient. Express using positive exponents.

9^4/9^5

1/9

Rewriting equivalent exponents

100

Write an expression using a positive exponent.

2/5*2/5*2/5*2/5

(2/5)^4

200

Find each quotient. Express using positive exponent.

(a^6)/(a^2)

a^4

300

What symbols make the statement true <,>, =?

4.1xx10^5 _ 3.7xx10^5

4.1xx10^5 >3.7xx10^5

400

What symbols make the statement true <,>, =?

2.8xx10^-1 _2.1xx10^1

2.8xx10^-1 <2.1xx10^1

500

Order each set  of numbers from least to greatest.

7.35xx10^4, 1.7xx10^-6, 8.26xx10^3, 9.3xx10^-2

1.7xx10^-6, 9.3xx10^-2, 8.26xx10^3, 7.35xx10^4

Scientific Notation

100

Express each number in scientific notation.

5.82 xx 10^3

5820

200

Express each number in scientific notation.

1.1 xx10^-4

0.00011

300

Express each number in scientific notation.

47,000

4.7xx10^4

400

Express each number in scientific notation. 

0.0072

7.2xx10^-3

500

Express each number in scientific notation. 

0.000561

5.61 xx10^-4

Unit 1 Fun

100

Evaluate each expression. Express the result in scientific notation.

(4.45xx10^9)(1.3xx10^6)

5.785xx10^15

200

Evaluate each expression. Express the result in scientific notation.

(5.85xx10^5)/(3.9xx10^-6)

1.5xx10^11

300

What operation do you use when the question asks, "how many times larger is ____ compared to ____"

Division

400

What error was made? What should the answer have been?

(1/3)(1/3)^2(1/3)^3 = (1/27)^6

someone multiplied all the bases together and added the exponents together instead of keeping the base and adding the exponents

answer: (1/3)⁶

500

A baby elephant weighs 2.2 x 10² pounds. An adult elephant weighs 1.0 x 10⁴ pounds. How many times larger is the adult elephant than the baby elephant?

(1.0 x 10⁴) / (2.2 x 10² ) = 4.54... x 10¹ times more (pounds)