Properties of Exponents - Easier Practice

Properties of Exponents

Easier Practice

The Product of Powers Property

• When the bases are the same, add the exponents to simplify

• The base is what "holds up" the exponent

Multiple Choice

Simplify

$$2^3\cdot2^3$$  

• $$2^4$$  

• $$2^6$$  

• $$2^5$$  

• $$2^3$$  

Multiple Choice

Let's step it up a notch...
Simplify:

$$x^3\cdot3x^2$$  

• $$x^3$$  

• $$3x^4$$  

• 2x

• $$3x^5$$  

Multiple Choice

Parentheses mean multiplication too....
Simplify:

$$\left(4m^2\right)\left(8m^5\right)$$  

• $$12m^7$$  

• $$32m^7$$  

• $$32m^{10}$$  

• $$12m^{10}$$  

The Power of a Power Property

• When a power is raised to another, a quick way to simplify is to multiply the exponents

• Only works for monomials

Multiple Choice

What was the answer to the last question? (4⁵)¹⁰

• $$4^{50}$$

• $$4^{15}$$

• $$20^{10}$$

• $$40^5$$

Multiple Choice

Simplify:

$$\left(2^3\right)^4$$  

• $$6^4$$  

• $$8^3$$  

• $$2^7$$  

• $$2^{12}$$  

Multiple Choice

Simplify:

$$\left(-x^5y^2\right)^4$$  

• $$8x^{12}y^6$$  

• 256

• $$x^{20}y^8$$  

• $$\frac{1}{256x^8y^{20}}$$  

Multiple Choice

Mix the properties!! Simplify:

$$10m^4\left(2m^3\right)^2$$  
**PEMDAS always applies**

• $$40m^{10}$$  

• $$20m^{10}$$  

• $$20m^9$$  

• $$40m^9$$  

Match

Match the following with their simplified answer.

• $$\frac{x^4}{x^2}$$

• $$x^{-5}$$

• $$\left(\frac{x^3}{x}\right)^{-2}$$

• $$\left(x^{100}\right)^0$$

• $$\left(\frac{1}{x^{-3}}\right)^4$$

x²

1

x¹²

• x²

• $$\frac{1}{x^5}$$

• $$\frac{1}{x^4}$$

• 1

• x¹²

Poll

How well do you understand properties of exponents?

• Very well!

• I mostly understand the problems.

• I still need practice.

• Not well!