Unit 2 Review - Exponents & Scientific Notation

Power & Product

100

What is the difference between the power rule and the product rule?

Power rule - multiply the exponents

Product rule - add the exponents

200

Simplify

(y²)^-4

1/y^8

300

Simplify

(y^7)(y^4)(y^-14)

1/y^3

400

What is the value of x?

p^3 * p^2 * p^x = p^10

x=5

500

Simplify

(2x⁴y⁶)²

4x⁸y¹²

Quotient

100

What operation do we perform when using the Quotient rule?

Subtraction

200

Simplify

d^12/d^2

d¹⁰

300

Which expression is equivalent to 

8^3/8^-8

A.  8^-11 

B.  1/8^5 

C.  8^11 

D.  8^-5 

C. 8¹¹

400

Simplify

2^-2/2^-6

2^4

500

What is the value of x?

5^12/5^x = 5^7

x=5

All Exponent Rules

100

Simplify

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

1/x^4

200

Simplify

(w^5*w^-2)/(w^3*w^3)

1/w^3

300

Simplify the expression completely,

(4^2 * 4^6)^3

2.814749767xx10^14

400

Write  1/4^2 as a:

Fraction

Whole number

Positive power

Negative power

Solve (no exponents) 

Fraction  1/4^2 

Whole number  4^-2 

Positive power  1/4^2 

Negative power  4^-2 

Solved  1/16 

500

Is the equation below true or false?

*Must show work*

(9^0 xx 9^5)/9^2 = ((9^3)^2)/9^3

True

9³ = 9³

Scientific Notation Conversions

100

Write the following numbers in scientific notation.

9,428,900,000,000

0.00000000002489

0.0789100034

9.4289 xx 10^12

2.489 xx 10^-11

7.89100034 xx 10^-2

200

Write the following numbers in standard form.

5.3891729 xx 10^8

4.98 xx 10^-5

3.2091 xx 10^10

538,917,290

0.0000498

32,901,000,000

300

Find the value of x in each problem.

A.    480,000 = 4.8 x 10^x

B.    0.00000238 = 2.38 x 10^x

C.    7,000,000 = 7 x 10^x

A.  x = 5

B.  x = -6

C. x = 6

400

Which number is the least in value?

Which number is the greatest in value?

A.  5.0 x 10^-9

B.  5.0 x 10^-8

C.  5.0 x 10^-6

D.  5.0 x 10^-4

Least Value = A.  5.0 x 10^-9

Greatest Value = D.  5.0 x 10^-4

500

List the numbers in order from least to greatest. Use the letters to list them.

A.  5.2E-4

B.  5.15E-3

C.  5.01E-3

D.  5.23E-4

Least

 A.   5.2E-4

 D.   5.23E-4

 C.   5.01E-3

 B.   5.15E-3

Greatest

Scientific Notation Operations

100

Solve the following equation. Write your answer in standard form.

(9xx10^4)+(1xx10^5)

190,000

200

Solve the following equation. Write your answer in scientific notation.

(3.45xx10^-3) - (2.68xx10^-7)

3.449732xx10^-3

300

Solve the following equation. Write your answer in scientific notation.

(8.2xx10^4)xx(2.7xx10^1)

2.214xx10^6

400

Solve the following equation. Write your answer in calculator notation.

(5.67xx10^20)/(9.84xx10^-6)

5.762195122E25

500

The dimensions of a rectangular office building are 1.5 x 10² feet by 1.35 x 10³ feet. What is the perimeter of the base of the building, in feet?

A.    3.00 x 10³

B.    2.85 x 10⁵

C.    5.70 x 10⁵

D.    1.50 x 10³

A.  3.00 x 10³

(1.5xx10^2)xx2=300

(1.35xx10^3)xx2=2700

2700+300=3000

Scientific Notation Story Problems

100

The River festival was a success! The river run had  9.37xx10^2 people, and the fireworks hosted   5.99xx10^3 people. 5,237 people attended the concert and  3.379xx10^3 attended the parade. Which event had the greatest attendance?

Fireworks

200

By area, Russia is the largest country in the world. It has an area of 8.649 x 10⁶ square miles. Canada is second with 4.797 x 10⁶ square miles. What is the difference in the areas? 

Write your answer in scientific notation.

3.852xx10^6

300

Students at Salt Lake Community College pay  1.585xx10^4  dollars for tuition. Students at George Washington University pay  4.573xx10^5  dollars. About how many times greater is the tuition at George Washington University than the tuition at Salt Lake C.C.? Round to hundredths place if necessary.

Write your answer in standard form and state the answer in the context of the problem.

Tuition at George Washington University is 28.85 times greater than Salt Lake Community College.

400

The diameter of the sun is 1.4 x 10⁶ kilometers. The diameter of the Earth is 1.28 x 10⁴ kilometers. About how many times bigger is the diameter of the sun than the diameter of the Earth? Round to the nearest whole number.

Write your answer in standard form and state the answer in the context of the problem. 

The diameter of the sun is about 109 times bigger than the diameter of the Earth.

500

This question has two parts.

Part A:

The mass of two animals at a zoom are described, where b and c are integers.

* The mass of a Northern Giraffe is 1,950,447 grams, or about   2xx10^b grams.

* The mass of a Plains Zebra is 399,161 grams, or about  4xx10^c  grams.

What are the values of b and c?

b = ?

c = ?

Part B

Using the estimated values, the mass of the Northern Giraffe is about  5xx10^m  times the mass of the Plains Zebra, where m is an integer.

What is the value of m?

m = ?

Part A:

b = 6  2xx10^6 

c = 5  4xx10^5 

Part B:

m = 0 5xx10^0