exponent properties and examples

Product of Powers

Words: when multiplying like bases, add the exponents

Symbols: (x^a)(x^b) = x^a+b

Numbers: (8³)(8⁶) = 8⁹

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Product of Power: Product Rule

The product rule states that when multiplying two numbers with the same base, you can add their exponents:

Poll

My level of understanding

(left to right, NO: I don't get it at all, Whoops: need some help but I'm starting to understand, Nailed It: I can do this on my own.

Multiple Choice

(2m³)(3m⁴) =

• 5m⁷

• 6m¹²

• 5m¹²

• 6m⁷

Power of a Power

Words: when a power (base with exponent) is raised to another power (exponent), you multiply the exponents (keep the base!)

Symbols: (x^a)^b= x^ab

Numbers: (8³)⁶=8¹⁸

Multiple Choice

Simplify:

$$\left(2^3\right)^4$$  

• $$6^4$$  

• $$8^3$$  

• $$2^7$$  

• $$2^{12}$$  

Multiple Choice

Simplify

$$\left(3a^2c\right)^3$$  

• $$9a^6c^3$$  

• $$27a^5c^3$$  

• $$27a^6c^3$$  

• $$9a^5c^3$$  

Power of a product (Distributive Rule)

Zero Exponent

Power of a Quotient

Quotient of Powers

Zero Exponent

Power of a Quotient

Quotient of Powers

Power of a Power

Words: when a power (base with exponent) is raised to another power (exponent), you multiply the exponents (keep the base!)

Symbols: (x^a)^b= x^ab

Numbers: (8³)⁶=8¹⁸

Power of a Product

Zero Exponent

Power of a Quotient

Quotient of Powers

Multiple Choice

Simplify:

$$\frac{5^7}{5^4}$$  

• $$5^{11}$$  

• $$1^3$$  

• $$5^3$$  

Power of a Product

Power of a Product: Example

Multiple Choice

Now it's your turn. $$\left(2ab\right)^3=?$$  

• $$2xy$$  

• $$2x^3y^3$$  

• $$8xy$$  

• $$8x^3y^3$$  

Power of a Power: Example

Multiple Choice

Now it is your turn. $$\left(t^6\right)^9=?$$  

• $$t^{15}$$  

• $$t^3$$  

• $$t^{-3}$$  

• $$t^{\frac{1}{3}}$$  

• $$t^{54}$$  

Multiple Choice

Your turn. What is $$\frac{\left(2x\right)^5}{\left(2x\right)^3}=?$$  

• $$4x^2$$  

• $$8x^2$$  

• $$1$$  

• $$16x^8$$  

​Simplify the following:

​Simplify the following:

Multiple Choice

Parentheses mean multiplication too....
Simplify:

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

• $$12m^7$$  

• $$32m^7$$  

• $$32m^{10}$$  

• $$12m^{10}$$  

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**

• $$40m^{10}$$  

• $$20m^{10}$$  

• $$20m^9$$  

• $$40m^9$$  

Poll

How well do you understand properties of exponents?

• Very well!

• I mostly understand the problems.

• I still need practice.

• Not well!

Multiple Choice

Simplify

$$\left(xy^5\right)^2$$  

• $$x^2y^{10}$$  

• $$x^2y^3$$  

• $$xy^3$$  

• $$xy^{10}$$  

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

My level of understanding

(left to right, NO: I don't get it at all, Whoops: need some help but I'm starting to understand, Nailed It: I can do this on my own.