Thursday Review: Exponents and Scientific Notation

Thursday Review: Exponents and Scientific Notation

Let's get ready for our quiz tomorrow!

Multiplying Powers

Shortcut: Add the exponents!

Multiple Choice

Simplify the following expression:

 $8^3\times8^5$  

•  $8^{15}$  

•  $8^8$  
  

•  $64^{15}$  

•  $64^8$  

Multiple Choice

Simplify the following expression:

 $x^{10}\cdot x^{12}$  

•  $x^{22}$  

•  $x^{120}$  

•  $x^2$  

• None of these.

Dividing Powers

Shortcut: Subtract the exponents!

Ask yourself: Is it top-heavy or bottom-heavy?

Multiple Choice

Simplify the following expression:

 $\frac{5^7}{5^3}$  

•  $5^4$  

•  $\frac{1}{5^4}$  

•  $5^{21}$  

•  $5^{10}$  

Multiple Choice

Simplify the following expression:

 $\frac{x^{10}}{x^{13}}$  

•  $\frac{1}{x^3}$  

•  $x^3$  

•  $x^{23}$  

•  $x^{130}$  

Powers of Powers

Shortcut: Multiply the exponents!

Multiple Choice

Simplify the following expression:

 $\left(10^2\right)^6$  

•  $10^{12}$  

•  $10^8$  

•  $10^{26}$  

•  $10^3$  

Multiple Choice

Simplify the following expression:

 $\left(x^3\right)^5$  

•  $x^8$  

•  $x^{15}$  

•  $x^{35}$  

•  $x^{12}$  

Negative Exponents

A negative exponent means it should be a bottom heavy fraction!

The exponent will be positive when it's in the bottom of the fraction.

Multiple Choice

Simplify the following expression:

 $11^{-5}$  

•  $\frac{1}{11^5}$  

•  $-55$  

•  $-\frac{1}{55}$  

•  $\frac{1}{11^{-5}}$  

Multiple Choice

Simplify the following expression:

 $x^{-10}$  

•  $\frac{1}{x^{10}}$  

•  $-\frac{1}{10}$  

•  $\frac{x}{10}$  

•  $\frac{10}{x}$  

Zero Exponents

Anything to the zero power will be equal to 1.

Everything has cancelled out and simplified to 1.

Multiple Choice

Simplify the following expression:

 $\left(-20\right)^0$  

•  $-20$   

•  $-1$  

•  $0$  

•  $1$  

Multiple Choice

Simplify the following expression:

 $x^0$  

•  $x$  

•  $0$  

•  $1$  

•  $1x$  

Let's put it all together!

Order of Operations:

1. Multiply parentheses

2. Move negative exponents to bottom

3. Add exponents.

4. Subtract exponents (top or bottom heavy???)

Multiple Choice

Simplify the following expression:

 $\frac{\left(x^5\right)^2}{x^7}$  

•  $x^0=1$  

•  $x^3$  

•  $\frac{1}{x^3}$  

•  $x^{-3}$  

Multiple Choice

Simplify the following expression:

 $\left(x^{-2}\right)^6$  

•  $x^{-12}=\frac{1}{x^{12}}$  

•  $x^4$  

•  $x^{-12}=-12x$  

•  $x^{12}$  

Multiple Choice

Simplify the following expression:

 $\frac{x^4\cdot x^{10}}{x^5}$  

•  $x^9$  

•  $\frac{1}{x^9}$  

•  $x^{35}$  

•  $x^{11}$  

Multiple Choice

Simplifying and evaluate the following expression:

 $\frac{3^5}{3^2\cdot3^6}$  

•  $\frac{1}{3^3}=\frac{1}{27}$  

•  $\frac{1}{3^3}=\frac{1}{9}$  

•  $\frac{1}{3^3}=27$  

•  $\frac{1}{3^3}=9$  

Multiple Choice

Simplify and evaluate the following expression: $\frac{10^4\cdot10^5}{\left(10^3\right)^3}$  

•  $10^0=1$  
  

•  $10^3=1000$  
  

•  $10^2=100$  

•  $10^{-1}=\frac{1}{10}$  

Scientific Notation

The exponent tells you how many times to move the exponent.

Positive exponent: move the decimal to the right.

Negative exponent: move the decimal to the left.

Multiple Choice

Write the following in standard notation:

 $5.23\times10^5$  

• 52,300,000

• 523,000

• 0.0000523

• 0.0523

Multiple Choice

Write the following in standard notation:

 $8.273\times10^{-4}$  

• 0.0008273

• 0.00008273

• 0.008273

• 82,730

Multiple Choice

Write the following in scientific notation:

 $7,100,000$  

•  $7.1\times10^6$  

•  $7.1\times10^5$  

•  $7.1\times10^{-5}$  

•  $7.1\times10^{-6}$  

Multiple Choice

Write the following in scientific notation:

 $0.0000031$  

•  $3.1\times10^{-6}$  

•  $3.1\times10^{-7}$  

•  $3.1\times10^{-8}$  

• None of these.

Multiply and Divide Scientific Notation

Multiple Choice

Simplify the following expression:

 $\left(1.2\times10^3\right)\left(3.3\times10^5\right)$  

•  $3.96\times10^8$  

•  $3.96\times10^{15}$  

•  $4.5\times10^8$  

•  $4.5\times10^{15}$  

Multiple Choice

Simplify the following expression:

 $\left(1.5\times10^{-3}\right)\left(5\times10^{-4}\right)$ 

•  $7.5\times10^{-7}$  

•  $7.5\times10^1$  

•  $6.5\times10^{-1}$  

•  $6.5\times10^{-7}$  

Multiple Choice

Simplify the following expression:

 $\frac{7.2\times10^3}{4\times10^5}$  

•  $1.8\times10^{-2}$  
  

•  $1.8\times10^{-1}$  
  

•  $1.8\times10^8$  

•  $1.8\times10^{-8}$  

Multiple Choice

Simplify the following expression:

 $\frac{9\times10^{10}}{3\times10^7}$  

•  $3\times10^3$  
  

•  $6\times10^3$  
  

•  $3\times10^{17}$  

•  $27\times10^{17}$  

Word Problems with Scientific Notation

1. Change both to standard form

2. Multiply or divide

3. Write in scientific notation

Multiple Choice

There are 1.2x10⁸ households in America. Each household uses 400 gallons of water each year. Determine how many total gallons of water American households use in a year.

What operation are you going to use?

• Multiplication

• Division

Multiple Choice

There are 1.2x10⁸ households in America. Each household uses 400 gallons of water each year. Determine how many total gallons of water American households use in a year.

• $4.8\times10^8\ gallons$

• $4.8\times10^9\ gallons$

• $4.8\times10^{10}\ gallons$

• $4.8\times10^7\ gallons$

Multiple Choice

The population of China is about 1.4x10⁹ people. Highlands has a population of 7,000 people. Determine how many times greater China's population is than Highlands.

What operation are you going to use?

• Multiplication

• Division

Multiple Choice

The population of China is about 1.4x10⁹ people. Highlands has a population of 7,000 people. Determine how many times greater China's population is than Highlands.

• $2\times10^5\ times\ greater$

• $2\times10^6\ times\ greater$

• $2\times10^7\ times\ greater$

• $2\times10^4\ times\ greater$