Section 2.3 - Properties of Exponents

​Section 2.3: Measure Up - Basic Exponent Rules

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​When two terms, with exponents, have the same base - you can simplify by adding the exponents when multiplying.

​DEFINITIONS:

Base: for this example is "a" it is the number that is raised to the power.

Exponent: the number in the SUPERSCRIPT position of a term. (Think "raised to...")​

Multiple Choice

Simplify to an equivalent expression BUT leave in exponent form:

$$4^3\cdot4^5$$  

• $$4^8$$  

• $$16^8$$  

• $$4^{15}$$  

• $$16^{15}$$  

Multiple Choice

Simplify the expression: 
c⁴⋅c³=

• ^c12
• c⁴⁺³
• c⁷

Multiple Choice

In order to multiply powers with the same base, we add their exponents. 

(i.e. x³ * x⁵ = x³⁺⁵ )

• True 
• False

​When two terms, with exponents, have the same base - you can simplify by subtracting the powers when dividing.

Multiple Choice

Simplify to an equivalent expression BUT leave in exponent form:

$$\frac{6^{26}}{6^4}^{ }$$  

• $$1^{22}$$  

• $$1^{30}$$  

• $$6^{22}$$  

• $$6^{30}$$  

Multiple Choice

Simplify to an equivalent expression;

$$\frac{x^6}{x^2}$$  

• x⁴

• x¹²

• x³

• x⁸

Multiple Choice

When dividing powers with the same base, you _______________ the exponents.

• Add

• Subtract

• Multiply

• Divide

​When a term with a power is raised to another power, you can multiply the powers to simplify.

Multiple Choice

Simplify the term.

(2⁸)²

• 2¹⁶
• 2¹⁰
• 2⁶
• 2⁴

Multiple Choice

Simplify the term;

$$\left(3^4\right)^7$$  

• $$3^{28}$$  

• $$3^3$$  

• $$3^{11}$$  

• $$12^7$$  

Multiple Choice

 

According to exponent rules, when we raise the power to a power we _______ the exponents. Example: (e²)⁵

• add

• subtract

• multiply

• divide

​When a term, with two different bases either multiplied or divided, is raised to a single power, the power can be distributed to both parts.

Multiple Choice

Simplify:

$$\left(xy^2z^3\right)^4$$  

• $$x^4y^8z^{12}$$  

• $$x^4y^6z^7$$  

• $$x^5y^6z^7$$  

• $$x^5y^8z^{12}$$  

Multiple Select

Which expression is equivalent (equal) to (x * y)⁶

• 6x * 6y

• x⁶ * y⁶

• x⁶y⁶

​

Some other rules to remember.​

Multiple Choice

Simplify

$$x^{-3}$$  

• $$\frac{1}{x^3}$$  

• $$x^3$$  

• $$\frac{1}{x^{-3}}$$  

• $$x$$  

Multiple Choice

Write as a radical

$$x^{\frac{4}{7}}$$  

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

• $$2a^2b^6$$

• $$\frac{1}{2a^2b^6}$$

• $$\frac{b^6}{2a^2}$$

• $$\frac{2b^6}{a^2}$$