Exponents and Scientific Notation Review

Exponent Rules

100

TRUE OR FALSE

4³ x 4⁵ = 4⁸

4³ x 4⁵ = 4¹⁵

TRUE

FALSE

200

TRUE OR FALSE

5³ x 5⁵ = 5¹⁵

5³ x 5⁵ = 25⁴

TRUE

FALSE

300

TRUE OR FALSE

4³ x 4⁵ = 16⁸

4² x 5² = 20⁴

FALSE

FALSE

400

2 × 10⁶   x   4.5 × 10^-2        

9 x 10⁴

500

12 × 10⁸   ÷   3 × 10³

4 x 10⁵

Scientific Notation

100

WRITE IN SCIENTIFIC NOTATION

70,000

7 x 10⁴

200

WRITE IN SCIENTIFIC NOTATION

0.007

7 X 10 ^-3

300

FIX THIS. WRITE IN SCIENTIFIC NOTATION.

70 x 10⁵

7.0 x 10⁶

400

FIX THIS. WRITE IN SCIENTIFIC NOTATION.

0.07 x 10^-5

7 x 10^-7

500

Is 70⁴ the same as 7 x 10⁴. EXPLAIN.

NO because

70⁴ = 70x70x70x70= 24,010,000

and 

7 x 10⁴ = 7x10x10x10x10= 70,000

Operations

100

About 1 x 10³ people live in Alaska. About 3 × 10⁸ people live in Texas. About how many more people live in Texas than live in Alaska?

About 3 x 10⁵ more people

200

There are about 2 million 8th grade students in the United States. They each send about 7300 texts a year. About how many stexts do all students send in one year? Express your answer in scientific notation.  

About 1.4 x 10¹⁰

300

There are about 57 million students in the United States. They each eat about 2200 school lunches over their schooling career. About how many school lunches do all students eat in one year? Express your answer in scientific notation.  

1.254 x 10¹¹

400

Here are the approximate masses of three planets, expressed in scientific notation: 

Mercury: 3.3×10²³; Venus: 4.87×10²⁴; Earth: 5.98×10²⁴.

Elena says that Earth has more than 10 times as much mass as Mercury. Is this correct? Explain how you know.

Yes, because it is about 18.12 times bigger.

(divide)

500

About 2.13 x 10⁷ people live in Florida. About 1.93×10⁶ people live in Nebraska. About how many more people live in Florida than live in Nebraska?

A)  1.937×10⁷

B)  2×10⁷

C)  2×10⁶

D)  1.937×10⁶

A)  1.937×10⁷

2.13 x 10⁷  -  1.93×10⁶ = 1.937×10⁷

Fill in the Blank

100

Place a number in each blank so that each equation is true.

4^{(  )}  x 4⁵ = 4¹²

4^{( 7 )}  x 4⁵ = 4¹²

200

Place a number in each blank so that each equation is true.

      5⁷

^{______________}  =  5^{(   )}

     5(  )

Answers Vary

Must use quotient rule. 

      5⁷

^{______________}  =  5^{(  10 )}

     5(-3)

300

Place a number in each blank so that each equation is true.

7^{(   )}  x 7^{(   )} = 2^{(   )} 

7^(-1)  x 7⁽⁺¹⁾= 2⁰

^{Any numbers work for the exponents if they are opposites.}

400

Place a number in each blank so that each equation is true.

5^-3 x (   )^-3 = 15^{(  )}

5^-3 x ( 3 )^-3 = 15^{( -3 )}

500

What 3 things does a number in scientific notation have to include?

Number 1-9.9

Multiplication

Power of 10

Number Lines(Must do in Order)

100

#1

25

200

#2

1x10²⁴        2x10²⁴         3x10²⁴,       etc.....

300

#3

Mercury (between 0 and 1), Venus (between 4 and 5), Earth (between 5 and 6)

400

#4

3.0X10^-3      3.1X10^-3     3.2X10^-3 ,   etc.....

500

#5

3.3X10^-3