Learning Rational Exponents

Remember, when you have an exponent that is a fraction, its power over root.

​

​Some text here about the topic of discussion.

​Rational Exponents

power

​

root

​

exponential form​

​

Multiple Choice

Which of the following is correct?

• $$\frac{Power}{Root}$$

• $$\frac{Root}{Power}$$

When simplifying, we must first convert to radical form.

​

​Some text here about the topic of discussion.

​Rational Exponents

power

​

root

​

exponential form​

​

radical form​

​

We don't write the "2" because it's implied!​

​

Multiple Choice

Which of the following is in radical form?

• $$\sqrt[4]{5^3}$$  

• $$5^{\frac{3}{2}}$$  

Multiple Choice

Which of the following is in exponential form?

• $$\sqrt[4]{8^{ }}$$  

• $$8^{\frac{1}{4}}$$  

Multiple Choice

Write the following expression in radical form: $$27^{\frac{2}{3}}$$  

• $$\sqrt[2]{27^3}$$  

• $$\sqrt[]{27^3}$$  

• $$\sqrt[3]{27^2}$$  

• $$\sqrt[]{27^2}$$  

Multiple Choice

Write the following expression in radical form: $$4^{\frac{5}{2}}$$  

• $$\sqrt[]{4^5}$$  

• $$\sqrt[5]{4^2}$$  

• $$\sqrt[5]{4}$$  

Multiple Choice

Write the following expression in radical form: $$81^{\frac{1}{2}}$$  

• $$\sqrt[]{81}$$  

• $$\sqrt[]{81^2}$$  

• $$\sqrt[1]{81^2}$$  

• $$81^2$$  

Multiple Choice

Write the following expression in radical form: $$64^{\frac{1}{3}}$$  

• $$\sqrt[]{64^3}$$   

• $$\sqrt[1]{64^3}$$   

• $$\sqrt[3]{64}$$  

Match

Match each expression to it's radical form:

• $$\sqrt[]{25^5}$$  

• $$\sqrt[5]{25^2}$$  

• $$\sqrt[]{5^{25}}$$  

• $$\sqrt[25]{5^2}$$  

 

 

 

 

• $$25^{\frac{5}{2}}$$  

• $$25^{\frac{2}{5}}$$  

• $$5^{\frac{25}{2}}$$  

• $$5^{\frac{2}{25}}$$  

For example:

​

​Some text here about the topic of discussion.

​When simplifying an expression with a rational exponent, take the root first!

​-Take the 5th root of 32 first

​-Now take the 2nd power

Multiple Choice

When simplifying an expression with a rational exponent, first we ...

• take the root

• take the power

Multiple Choice

Which of the following orders is correct when simplifying expressions with rational exponents?

• Take the root, then the power.

• Take the power, then the root.

Multiple Choice

Which of the following steps would you take when simplifying the expression $$\sqrt[]{25^3}$$

• Raise 25 to the 3rd power, then take the square root.

• Take the square root of 25, then raise it to the 3rd power.

Match

Match the following:

• 16

• 4

• 64

• 9

• 81

 

 

 

 

 

• $$\sqrt[3]{8^4}$$  

• $$\sqrt[4]{16^2}$$  

• $$\sqrt[]{16^3}$$  

• $$\sqrt[4]{81^2}$$  

• $$\sqrt[3]{27^4}$$  

For example:

​

​Some text here about the topic of discussion.

If the expression is written in exponential form, convert it to radical form in order to simplify it.

exponential form​

​

radical form​

​

2.) Take the "root" ​

​

1.) Write in radical form​

​

3.) Take the "power" ​

​

Reorder

Reorder in the order when simplifying $$8^{\frac{2}{3}}$$ :

• $$8^{\frac{2}{3}}$$  

• $$=\sqrt[3]{8^2}$$  

• $$=2^2$$  

• $$=4$$  

1

2

3

4

• 1
• 2
• 3
• 4

Multiple Choice

Simplify: $$8^{\frac{4}{3}}$$  

• 2

• 8

• 16

• 4

Multiple Choice

Simplify: $$16^{\frac{1}{2}}$$  

• 4

• 8

• 32

• 16