Power to a Power Property

Power to a Power Property

by Ebony Smith

​Goals

• ​Learning Target: we will learn about the properties of exponents

• ​Success Criteria: I can use the properties of exponents to simplify expressions

​So far, we have already learned about two properties--Product and Quotient

1. ​Product Rule/Property: if we have like bases, we keep the base(s) and add the exponents.

   1. ​If there are coefficients, we multiply them

2. ​Quotient Rule/Property: if we have like bases, we keep the base(s) and subtract the exponents.

   1. ​if there are coefficients, we divide them

Multiple Choice

Simplify using the product property

$$a^5\cdot a^8=$$  

• $$a^3$$  

• $$a^{-3}$$  

• $$a^{13}$$  

• $$a^{40}$$  

Multiple Choice

Simplify using the product property

$$x^2y^2z^3\left(yz^2\right)=$$  

• $$x^2y^3z^6$$  

• xyz

• $$x^22y^22z^5$$  

• $$x^2y^3z^5$$  

Multiple Choice

Simplify using the product property

$$3lmn^2\cdot4l^3m^5=$$  

• $$12l^4m^6n^2$$  

• $$7l^4m^6n^2$$  

• $$7l^3m^5n^2$$  

• none of these are correct

Multiple Choice

Simplify using the quotient property

$$\frac{a^6}{a^3}=$$  

• $$a^2$$  

• $$a^3$$  

• $$a^{18}$$  

• 3

Multiple Choice

Simplify using the quotient property: $$\frac{x^2y^8}{xy}$$  

• $$xy^7$$  

• $$xy$$  

• $$x^3y^9$$  

• $$x^3y^7$$  

Multiple Choice

True or False?

• True
• False

​Power to a Power

​When we have an exponent raised to a power, we keep the base and multiply the exponents.

​Why the rule works...

Multiple Choice

Simplify using to power to a power property (x³)⁴

• x¹²

• x^-1

• x⁷

• x⁰

Multiple Choice

Simplify using to power to a power property

(2²)³

• 2⁵

• 2^-1

• 2⁶

• 2⁰

Multiple Choice

Simplify using to power to a power property

(y⁵)²

• y³

• y¹⁰

• y⁷

• y⁰

Multiple Choice

Simplify using to power to a power property

(z¹⁰)³

• z⁰

• z⁷

• z¹³

• z³⁰

​If there are more than 1 base...

Multiple Choice

Simplify:
(xy²)⁴

• x⁴y²
• x⁴y⁸
• x³y²
• x⁵y⁶

​If there is a coefficent...

Multiple Choice

Simplify:
(5ab²)²

• 25a²b⁴
• 10a²b⁴
• 5a²b⁴
• 25ab²

Multiple Choice

Simplify:
(7y⁴)²

• 7y⁶
• 14y⁸
• 14y⁶
• 49y⁸