Properties of Exponents

Properties of Exponents

Let's learn the properties of exponents. You'll want to take notes as you go so that you can answer all of the questions.

Product of Powers

Product of Powers: Example

Multiple Choice

Your turn: product of powers. What is $$y^6\cdot y^2$$ ?

• $$y^{6+2}$$  

• $$y^{6-2}$$  

• $$y^{6\div2}$$  

• $$y^{6\times2}$$  

Multiple Choice

$$z^3\cdot z^7=?$$  

• $$z^{21}$$  

• $$z^{\frac{3}{7}}$$  

• $$z^{-4}$$  

• $$z^{10}$$  

• $$z^4$$  

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

Power of a Power: Example

Multiple Choice

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

• $$t^{15}$$  

• $$t^3$$  

• $$t^{-3}$$  

• $$t^{\frac{1}{3}}$$  

• $$t^{54}$$  

Power of a Zero

Power of a Zero: Examples.

Fill in the Blank

What is $$42^0?$$  

Fill in the Blank

What is $$\left(38k\right)^0?$$  

Quotient of Powers

Quotient of Powers: Example.

Multiple Choice

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

• $$4x^2$$  

• $$8x^2$$  

• $$1$$  

• $$16x^8$$  

Power of a Quotient

Power of a Quotient: Example

Multiple Select

Now it is your turn. $$\left(\frac{2s}{r}\right)^4=?$$  Select all that are right.

• $$\frac{\left(2s\right)^4}{r^4}$$  

• $$\frac{16s^4}{r^4}$$  

• $$\frac{8s^4}{r^2}$$  

• Cannot be simplified

Negative Exponents.

Negative Exponents Examples.

Multiple Choice

Your turn. What is $$y^{-12}?$$  

• $$y^{12}$$  

• $$\frac{1}{y^6}$$  

• Cannot be simplified. 

• $$\frac{1}{y^{12}}$$  

Multiple Choice

(3⁴)(3⁷)

• 3²⁸
• 3³
• 3^-3
• 3¹¹

Multiple Choice

(x⁸)(x^-5)

• x^-40
• x^-13
• x¹³
• x³

Multiple Choice

(5⁸) / (5³)

• 5⁵
• 1⁵
• 5¹¹
• 1¹¹

Multiple Choice

(8⁵)³

• 8⁸
• 8¹⁵
• 8²
• 1/8²

Multiple Choice

(t^-6)^-5

• t^-11
• t^-30
• t³⁰
• t¹¹

Multiple Choice

4^-8

• 1⁸/4
• 4⁸/1
• 4/1⁸
• 1/4⁸

Multiple Choice

7⁰

• 7¹
• 0¹
• 1
• 7

Multiple Choice

(3x)⁰

• (3x)¹
• 0¹
• 1
• 3x

Multiple Choice

Simplify the following expression: 
xy^-7

• xy⁷
• x/y⁷
• x⁷/y
• x⁷y

Multiple Choice

Anything raised to a power of zero is always: 

• 0
• 1
• itself
• negative

Multiple Choice

According to exponent rules, when we raise the power to a power we _______ the exponents.

• add
• subtract
• multiply
• divide

Multiple Choice

• 2 / x²
• -2x²
• 2x²
• 2x¹⁴

Multiple Choice

According to exponent rules, when we multiply the expressions we _______ the exponents.

• add
• subtract
• multiply
• divide

Multiple Choice

According to exponent rules, when we divide the expressions we _______ the exponents.

• add
• subtract
• multiply
• divide

Multiple Choice

Fill in the blank with the correct exponent to make the statement true.
3^{16 =} (3⁸)(3^_)

• 2
• 8
• 4
• 1

Multiple Choice

Simplify the exponential expression.

• 2x⁶y¹²
• 2x⁵y⁷
• 8x⁶y¹²
• 8x⁵y⁷

Multiple Choice

Simplify (-4r⁵)(2r⁸)

• -8r¹³
• -2r¹³
• -8r⁴⁰
• -2y⁴⁰

Multiple Choice

• a
• b