Review - Exponent and Logarithm Rules and Properties

Review: Exponent Rules and Properties

The following slide provide an overview of exponent rules and properties. Please review before continuing to the next activity.

When raising a power to another power, multiply the exponents.

​Power Rule

Any non-zero base raised to the power of zero equals 1.

A fractional exponent represents a root. The denominator is the root, and the numerator is the power. 

When multiplying with the same base, add the exponents.

​Product Rule

When dividing with the same base, subtract the exponents.

Quotient Rule

Zero Exponent Rule

​Negative Exponent Rule

​Fractional Exponent Rule

A negative exponent means take the reciprocal and make the exponent positive.

Any base raised to the power of 1 is itself.

Exponent of 1

Match

Match the following

Exponent of 1

Negative Exponent Rule

Power Rule

Product Rule

• Exponent of 1

• Negative Exponent Rule

• Power Rule

• Product Rule

Match

Match the following

Quotient Rule

Fractional Exponent Rule

Zero Exponent Rule

• Quotient Rule

• Fractional Exponent Rule

• Zero Exponent Rule

Multiple Choice

Simplify $$3^2\cdot3^3$$

• $$3^5$$

• $$3^6$$

• $$9^5$$

• $$6^5$$

Math Response

Simplify $$\frac{5^6}{5^2}$$

Type answer here

Correct Answer: 5^4

Deg^°

Rad

Drag and Drop

The expression $$7^0$$ simplifies to ​

Placeholder

Drag these tiles and drop them in the correct blank above

1

0

7

Undefined

Math Response

Simplify $$\left(2^3\right)^4$$

Type answer here

Correct Answer: 2^{12}

Deg^°

Rad

Drag and Drop

The expression $$4^{-2}$$ is equivalent to​ ​

Placeholder

which is equal to​ ​

Placeholder

Drag these tiles and drop them in the correct blank above

Multiple Choice

Simplify $$9^1$$

• 81

• 1

• 9

• 10

Drag and Drop

The expression $$8^{\frac{2}{3}}$$ is equivalent to​ ​

Placeholder

which is equal to​ ​ ​

Placeholder

.

Drag these tiles and drop them in the correct blank above

16

64

2

4

Review: Logarithm Rules and Properties

The following slide provide an overview of logarithm rules and properties. Please review before continuing to the next activity.

The logarithm of a quotient is the difference of the logarithms.

Quotient Rule

The logarithm of a number raised to an exponent is the exponent times the logarithm of the base.

The logarithm of 1 in any base is 0.

A logarithm answers the question: "To what power must the base b be raised to get x?"

​Definition of a Logarithm

The logarithm of a product is the sum of the logarithms.

Product Rule

Power Rule

Change of Base Formula

Logarithm of 1

To evaluate a logarithm with a different base, you can rewrite it using the change of base formula.

The logarithm of a base to itself is 1.

Logarithm of the Base

Match

Reorder the following

Logarithm of 1

Logarithm of the Base

Definition of a Logarithm

Quotient Rule

• Logarithm of 1

• Logarithm of the Base

• Definition of a Logarithm

• Quotient Rule

Match

Reorder the following

Change of Base Formula

Product Rule

Power Rule

• Change of Base Formula

• Product Rule

• Power Rule

Math Response

Evaluate $$\log_2\left(8\right)$$

Type answer here

Correct Answer: 3

Deg^°

Rad

Drag and Drop

The expression $$\log_3\left(\frac{27}{9}\right)$$ simplifies to the expression​

Placeholder

Placeholder

​

Placeholder

Drag these tiles and drop them in the correct blank above

-

/

*

+

Multiple Choice

Simplify $$\log_2\left(4\cdot8\right)$$

• $$\log_2\left(32\right)$$

• $$\log_2\left(4\right)\cdot\log_2\left(8\right)$$

• $$\log_2\left(4\right)+\log_2\left(8\right)$$

• $$\log_2\left(12\right)$$

Multiple Choice

Simplify $$\log_2\left(10\right)$$ using the change of base formula.

• $$\frac{\log\left(2\right)}{\log\left(10\right)}$$

• $$\frac{\log\left(10\right)}{\log\left(2\right)}$$

• $$\log\left(10\right)-\log\left(2\right)$$

• $$\frac{\log_2\left(10\right)}{\log_2\left(2\right)}$$

Multiple Choice

Simplify $$\log_2\left(8^2\right)$$

• $$2\cdot\log_2\left(8\right)$$

• $$8\cdot\log_2\left(2\right)$$

• $$16\cdot\log_2\left(8\right)$$

• $$\log_2\left(64\right)$$

Dropdown

The expression $$\log_5\left(1\right)$$ = ​

Select answer

.

Math Response

Evaluate $$\log_7\left(7\right)$$ .

Type answer here

Correct Answer: 1

Deg^°

Rad