Law of Exponents: Product and Quotient Rule

​LAWS OF EXPONENTS

​Weekly Objective: Students will use reasoning to define the laws of exponents to simplify expressions with exponents by applying the including:

----Product Rule
----Quotient Rule
--Power Rule


with an at least 75% accuracy.

True Meaning of Exponent

Product Rule

Vocabulary Review

Base:
a number that is raised to a certain power

Exponent:
Shows how many times the number is multiplied by itself.

Coefficient:
a number that multiplied by the variable

Exponents

Let's review exponents!

Product Rule

Quotient Rule

Power Rule Investigation

Hint: Utilize expansion to help determine

Could you create a rule to simplify the expression?

Rule: 

Power Rules: Investigation

Power to a Power rule

Power Rule

Multiple Choice

Simplify the following expression:

(b³)⁸

• b¹¹

• 8b³

• b²⁴

• 24b

Multiple Choice

Which shows the Power Rule used correctly?  $$\left(ab\right)^5$$  

• $$ab^5$$  

• $$a^5b^5$$  

• $$a^5b$$  

• $$a^6b^6$$  

Multiple Choice

$$\left(x^5y^7\right)^3\ =\ x^{15}y^{21}$$  

• True

• False

Multiple Choice

Simplify the exponential expression. $$\left(\left(-2\right)^5\right)^8$$  

• $$\left(-2\right)^{40}$$  

• $$\left(-2\right)^{13}$$  

• $$\left(-2\right)^3$$  

• $$\left(-2\right)^{16}$$  

Just like when before the variable terms may have a Coefficient

Multiple Choice

Simplify the exponential expression. $$\left(3^2a^4\right)^5$$  

• $$3^{10}a^9$$  

• $$3^{10}a^{20}$$  

• $$3^7a^9$$  

• $$3^7a^{20}$$  

Multiple Choice

Simplify. $$\left(2cd^2\right)^4$$  

• $$2^4c^4d^6$$  

• $$2^4c^4d^8$$  

Multiple Choice

$$\left(3n^4\right)^3$$  

• $$9n^{12}$$  

• $$9n^7$$  

• $$27n^7$$  

• $$27n^{12}$$  

Multiple Choice

Simplify the following expression:

(3x³y⁵)⁴

• 3x¹²y²⁰

• 81x¹²y²⁰

• 12x¹²y²⁰

• 81x⁷y⁹

Let's mix them up the Laws!

Multiple Choice

Simplify.

-(2xy)(4x²y⁵)²

• -32x⁵y¹¹

• 32x⁵y¹¹

• -32x⁵y⁸

• -16x⁵y¹¹

Multiple Choice

Simplify.

3(-2x³y⁴)⁴

• 48x¹²y¹⁶

• -48x¹²y¹⁶

• -24x¹²y¹⁶

• -24x⁷y⁸

Multiple Choice

Simplify $$\left(\frac{6c}{d}\right)^3$$

• $$\frac{6c^3}{d^3}$$

• $$\frac{216c^3}{d^3}$$

• $$\frac{36c^3}{d^3}$$

• $$\frac{216c^3}{d}$$

Multiple Choice

Simplify $$\left(\frac{cd^2}{d}\right)^5$$

• $$\frac{cd^{10}}{d^{ }}$$

• $$\frac{c^5d^{10}}{d^{ }}$$

• $$c^5d^{10}$$

• $$c^5d^5$$