Laws of Exponents - Quotient Rule Part II

Quotient Law

* Divide the coefficients
(number divided by number) to simplify the number fraction

* Subtract the exponents
(LIKE variable subtract powers)

Multiple Choice

Quotient Rule: For LIKE BASES, keep the base the same and __________exponents.

• multiply

• add

• subtract

• divide

Multiple Choice

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

• add
• subtract
• multiply
• divide

Multiple Choice

• F

• G

• H

• J

Multiple Choice

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

• add

• subtract

• multiply

• divide

Multiple Choice

• A

• B

• C

• D

Multiple Choice

Simplify using the Laws of Exponents:

Multiple Choice

$$\frac{\ \ \ x^{15}\ \ \ }{y^{12}}$$  

• $$xy^3$$  

• $$x^{27}$$  

• Not like bases, laws of exponents can not be applied 

• $$y^3$$  

Multiple Choice

$$\frac{30y^{12}}{15y^2}$$  

• $$2y^{24}$$  

• $$2^{10}$$  

• $$2y^{10}$$  

• $$2y^{14}$$  

Multiple Choice

Simplify:

• $$\frac{5p^3}{3}$$

• $$5p^3$$

• $$3p$$

• $$10p^4$$

Multiple Choice

Simplify:

Mixed Review

Multiple Choice

Simplify the following expression:

5a³b⁵ ⋅ 3a²b²

• 8a⁵b³

• 15a⁵b⁷

• 8a⁵b⁷

• 15a⁵b³

Multiple Choice

Simplify the following expression:

c⁴ ⋅ c³

• c¹²

• c⁴³

• c⁷

• c¹

Multiple Choice

Simplify the following expression:

(7a²)(5a⁶b)²

• 35a¹⁴b²

• 175a¹²b²

• 175a¹⁴b²

• 35a¹⁴b

Multiple Choice

Evaluate the expression using the quotient of powers rule.

• a⁸b¹³
• a²b⁷
• a¹⁵b³⁰
• a⁸b⁷

Multiple Choice

Anything raised to a power of zero is always: 

• 0
• 1
• itself
• negative

Multiple Choice

(5³x²y⁴)⁰

• 5xy
• 1
• 0
• 5

Multiple Choice

(7v³)(10u³v⁵)

• 70u³v⁶

• 17u³v⁸

• 70u³v⁸

• none of the above

Multiple Choice

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

• Multiply
• Add
• Divide
• Subtract

Multiple Choice

Simplify $$\left(-x^3\right)\left(-7x^5\right)$$  

• $$7x^8$$  

• $$-7x^{15}$$  

• $$-7x^8$$  

• $$7x^{15}$$  

Multiple Choice

How do you solve:
(2x⁵)(6x⁴)

• MULTIPLY coefficients
  MULTIPLY exponents
• DIVIDE coefficients
  SUBTRACT exponents
• Combine like terms
• MULTIPLY coefficients
  ADD exponents

Multiple Choice

Which expression represents the product of $$\left(2x^2y^2\right)\left(3x^3y^3\right)$$ ?

• $$6x^6y^6$$  

• $$5x^5y^5$$  

• $$5x^6y^6$$  

• $$6x^5y^5$$  

Multiple Choice

Which expression is equivalent to $$\frac{x^2y^2z^2}{4y^4}$$ ?

• $$4y^6$$  

• $$y^6$$  

• $$\frac{x^2z^2}{4y^2}$$  

• $$4x^2y^6z^2$$  

Multiple Choice

Simplify: $$\frac{12r^{15}}{2r^3}$$  

• $$72r^3$$  

• $$72r^{27}$$  

• $$6r^3$$  

• $$6r^{12}$$  

Multiple Choice

Simplify:
(x⁵)⁴

• x⁹
• x²⁰
• x
• x⁵⁴

Drag and Drop

$$\left(12a^2b^{-1}c^4\right)\left(3a^3b^5c^{-2}\right)$$  is equivalent to which of the following?

Placeholder

Drag these tiles and drop them in the correct blank above

Multiple Choice

$$4z^4\cdot6z^{-6}$$  

• $$\frac{24}{z^2}$$  

• $$24z^{-24}$$  

• $$\frac{10}{z^2}$$  

• $$10z^{-24}$$  

Multiple Choice

$$\left(m^7\right)^4\cdot m^3$$  

• $$m^{28}$$  

• $$m^{14}$$  

• $$m^{84}$$  

• $$m^{31}$$  

Multiple Choice

$$\left(\frac{3x^4}{y^6}\right)^5$$  

• $$\frac{15x^{20}}{y^{30}}$$  

• $$\frac{3x^{20}}{y^6}$$  

• $$\frac{243x^{20}}{y^{30}}$$  

• $$\frac{243x^9}{y^{11}}$$  

Dropdown

BONUS: (SHOW WORK !)



The area of a rectangle is $$72r^5s^2t^7$$ square units. If the length if the rectangle is  $$3r^2t^4$$ units, what is therectangle's width?

Select answer