Properties of Exponents Lesson

​P2: Properties of Exponents

Multiple Choice

According to exponent rules, when we multiply two power with the same base we _______ the exponents. #1

Example: c⁶ ⋅ c⁴

• add

• subtract

• multiply

• divide

Multiple Choice

4³ x 4³

^#16

• 4⁶

• 4⁹

• 16⁶

• 16⁹

Multiple Choice

Simplify:  (x⁸)(x^-5)

#13

• x^-40

• x^-13

• x¹³

• x³

Multiple Choice

According to exponent rules, when we raise a power to a power we _______ the exponents. Example: (d²)⁵

^#2

• add

• subtract

• multiply

• divide

Multiple Choice

Select the expression that is equivalent (equal) to (7⁶)⁴. #5

• 7¹⁰

• 7²

• 7²⁴

• 7²⁷

Multiple Choice

Anything raised to a power of zero is always: #22

• 0

• 1

• itself

• negative

Multiple Choice

(34x⁵y⁶z^-7)⁰

^#29

• 34x⁵y⁶ / z⁷

• 34x⁵y⁶ / x^-7

• 0

• 1

Multiple Choice

According to exponent rules, when we divide two powers with the same base we _______ the exponents. Example: h⁸ / h³

^#4

• add

• subtract

• multiply

• divide

Multiple Choice

Select the expression equivalent (equal) to $$\frac{6^8}{6^3}$$  . #7

• $$6^{11}$$  

• $$6^5$$  

• $$6^{24}$$  

• $$6^{-5}$$  

Multiple Choice

Which expression is equivalent (equal) to $$\frac{10^{-3}}{10^9}$$  .#11

• $$10^{-12}$$  

• $$10^{-6}$$  

• $$10^6$$  

• $$10^{-27}$$  

Multiple Choice

 Simplify the expression using the properties of exponents.     $$\frac{t^{12}u^7}{t^2u}$$  #14

• $$t^{14}u^8$$  

• $$t^{24}u^7$$  

• $$t^{10}u^7$$  

• $$t^{10}u^6$$  

Multiple Choice

Which expression is equivalent (equal) to $$\frac{\left(6^{-4}\right)^{-2}}{6^2}$$  .#12

• $$6^6$$  

• $$6^{-10}$$  

• $$6^{-8}$$  

• $$6^{10}$$  

Multiple Choice

Simplify:

$$\left(xy^2z^3\right)^4$$  

• $$x^4y^8z^{12}$$  

• $$x^4y^6z^7$$  

• $$x^5y^6z^7$$  

• $$x^5y^8z^{12}$$  

​

Some other rules to remember.​

Multiple Choice

Simplify

$$x^{-3}$$  

• $$\frac{1}{x^3}$$  

• $$x^3$$  

• $$\frac{1}{x^{-3}}$$  

• $$x$$  

Match

Match the following

• $$\left(\frac{x}{y}\right)^3$$  

• $$\frac{1}{x^3}$$  

• $$x^0$$  

x³/y³

x^-3

1

• x³/y³

• x^-3

• 1

Multiple Choice

How do you simplify:

HINT: Apply the indicated operation to like factors of each term.

$$\left(2x^5\right)\left(3x^6\right)$$   

• MULTIPLY coefficients

  MULTIPLY exponents

• DIVIDE coefficients

  SUBTRACT exponents

• Combine like terms

• MULTIPLY coefficients

  ADD exponents

Multiple Choice

Simplify:  $$\left(7x^4\right)\left(9x^3\right)$$  

• $$16x^{12}$$  

• $$79x^{12}$$  

• $$63x^7$$  

• $$63x^{12}$$  

Multiple Choice

Simplify:

$$\left(2x^2\right)^3$$  

• $$2x^6$$  

• $$8x^5$$  

• $$6x^6$$  

• $$8x^6$$  

Multiple Choice

Simplify:

$$\frac{14x^7}{7x}$$  

• $$2x^6$$  

• $$2x$$  

• $$2x^5$$  

• $$2x^8$$  

Multiple Choice

Simplify: $$\left(xy^2z^3\right)\left(3x^4y^6z^8\right)$$  

• $$3x^0y^{12}z^{24}$$  

• $$3x^5y^8z^{11}$$  

• $$3x^4y^8z^{11}$$  

• $$3x^4y^{12}z^{24}$$  

Multiple Choice

• $$2a^2b^6$$

• $$\frac{1}{2a^2b^6}$$

• $$\frac{b^6}{2a^2}$$

• $$\frac{2b^6}{a^2}$$

Multiple Choice

Write $$\frac{1}{5^{-3}}$$  using a positive exponent.

• $$\frac{1}{5^3}$$  

• $$5^3$$  

• 5

• $$\frac{1}{5}$$  

Multiple Choice

Write the expression using a positive exponent $$b^{-3}$$  

• $$b^3$$  

• $$\frac{1}{b^{-3}}$$  

• $$\frac{1}{b^3}$$  

• $$\frac{1}{b}$$  

Multiple Choice

Simplify 1,999,252,111⁰

• 1,999,252,111

• 0

• 1

• Infinity

Multiple Choice

Mix the properties!! Simplify:

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

• $$40m^{10}$$  

• $$20m^{10}$$  

• $$20m^9$$  

• $$40m^9$$  

Multiple Choice

Challenge One! Simplify:

$$\left(-x^5y^2\right)^4$$  

• $$8x^{12}y^6$$  

• 256

• $$x^{20}y^8$$  

• $$\frac{1}{256x^8y^{20}}$$  

Multiple Select

Select ALL expressions equivalent to

$$\left(4^5\cdot4^{-3}\right)^{-2}$$  .

• $$\frac{1}{256}$$  

• 256

• $$4^{-10}\cdot4^6$$  

• $$4^{-3}\cdot4^{-5}$$  

Multiple Select

Which of these equations is correct? Select all that apply.

• $$2^{-2}\cdot2^8=64$$

• $$3^{-5}\cdot3^1=\frac{1}{81}$$

• $$4^4\cdot4^{-3}=4$$

• $$5^3\cdot5^{-1}=\frac{1}{125}$$