Properties of Exponents

Properties of Exponents

Let's learn and practice​

By R. Burrell

Draw

Circle the error(s) and find f(-2).

​UNIT QUESTION: How do I justify and solve the solution to a system of equations or inequalities?

Standard: MGSE9-12.A.REI.1, 3, 5, 6, and 12

​

Today’s Question:

How do I solve an exponential equation algebraically?

Standard: MGSE9-12.A.REI. 1 & 3

Exponents Basic Review

​Properties of Exponents

Basic Properties of Exponents 

Anything raised to the 1st power is itself!​

Basic Properties of Exponents 

Converting from Exponential Form to Expanded Form to Standard Form

​

Multiple Choice

The Ones Rules

A. A number raised to one is always that number.

B. One ________to any number I always one.

• number

• subtracted

• adding

• raised

Multiple Choice

5², What is the exponential expanded form for this equation?

• $$5\cdot5$$  

• $$2\cdot2\cdot2\cdot2\cdot2$$  

Multiple Choice

Which is GREATER?

2⁷ or 7²

• 2⁷

• 7²

• Neither, they are equal

Multiple Choice

2⁵ is the same as (2)(5).

• True

• False

Multiple Choice

True or False?

2 x 2 x 2 x 2 = (-2) x (-2) x (-2) x (-2)

• True

• False

Properties of Exponents 

​

​Anything raised to the "Zero" power is 1!

*except 0

Multiple Choice

Anything raised to a power of zero is always: 

• 0

• 1

• itself

• negative

Multiple Choice

Which is greater,  2654⁰ or 5⁰?

• 2654⁰

• 5⁰

• They are the same

• Zero is greater

Properties of Exponents 

​

​A number raised to a negative power is equal to one over the number raised to the positive opposite power.

Multiple Choice

When you have a negative exponent, take the reciprocal of the base and exponent. Always get rid of the ____________exponents in an expression.

• zero

• negative

• positive

• variable

Multiple Choice

Simplify 4^-2= 

• $$\frac{1}{4}$$  

• $$\frac{1}{16}$$  

• -16

• -8

Multiple Choice

Simplify $$\frac{1}{3^{-4}}$$  = 

• $$\frac{1}{81}$$  

• $$\frac{1}{12}$$  

• 81

• -81

Multiple Choice

Simplify x^-3

• -x³

• 1 / x^-3

• 1 / x³

• -x^-3

Multiple Choice

Simplify the following expression: xy^-7

• xy⁷

• x/y⁷

• x⁷/y

• x⁷y

Properties of Exponents ​

The product of like bases says the product of two exponent terms with the same base is the base raised to the sum of the exponents

Multiple Choice

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

• True

• False

Multiple Choice

Simplify the expression: c⁴⋅c³=

• $$c^{12}$$  

• $$c^{4+3}$$  

• $$c^7$$  

• $$7^c$$  

Multiple Choice

Simplify the expression: 3x²⋅5x²=

• $$15x^{ }$$  

• $$15x^{2+2}$$  

• $$8x^4$$  

• $$15x^4$$  

Properties of Exponents ​

The power rule for exponents says that raising a power to power is the same as multiplying the exponents together.

Multiple Choice

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

• add

• subtract

• multiply

• divide

Multiple Choice

Simplify: (2⁸)²

• $$2^{16}$$  

• $$2^4$$  

• $$2^{10}$$  

• $$\left(2^8\right)\left(2^8\right)$$  

Properties of Exponents ​

The product to a power rule for exponents says that raising the product of two numbers to power is the same as raising the two numbers to the same power before multiplying.

Multiple Choice

When raising a product to a power, __________ the exponents to each factor in the product. Then simplify the expression.

• distribute

• add

• multiply

• divide

Multiple Choice

Simplify:  (2ab)³

• $$6a^3b^3$$  

• $$8a^3b^3$$  

• $$2ab^3$$  

• 8ab

Properties of Exponents ​

The quotient of like bases says if we have exponents with the same base being divided, we can just subtract the exponents.

Multiple Choice

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

• add

• subtract

• multiply

• divide

Multiple Choice

Simplify: x⁶ / x²

• $$x^3$$  

• $$x^8$$  

• $$x^{12}$$  

• $$x^4$$  

Multiple Choice

Simplify: 18h¹⁰/ 6h⁸ 

• $$3h^{18}$$  

• $$3h^{80}$$  

• $$2h^2$$  

• $$3h^2$$  

Properties of Exponents ​

The quotient to a power rule for exponents says that raising the quotient of two numbers to power is the same as raising the two numbers to the same power before dividing.

Multiple Choice

When raising a quotient to a power, distribute the _____________ to the numerator and denominator. Then simplify the expression.

• exponent

• numbers

• integers

• name

Multiple Choice

Simplify: (x⁵/y⁶)²

• x⁹/y⁴

• x¹⁰/y¹²

• x⁶/y⁴

• x^2.5/y³

Multiple Choice

Simplify: (12x⁵y⁴/16x²y⁶)²

^{Note: / is divide--rewrite first part over the second part to view easier}

• 9x⁹/16y⁴

• 144x¹⁰y⁸/256x⁴y¹²

• 3x⁶/4y⁴

• 9x⁶/16y⁴

Poll

My level of understanding

(left to right) NO: I don't get it at all, Whoops: need some help but I'm starting to understand, Nailed It: I can do this on my own.

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​Find Common(Same) Base:

Convert Standard to Exponential Form

Multiple Choice

Solve for x using the same base method.(-3)^x = (-3)¹³

• 13

• -3

• x-13

• x+13

Multiple Choice

Solve for x using the same base method. 2^x = 4^x+1

• -2

• -3

• 2

• 3

Multiple Choice

Solve for x using the same base method. 7^-x = 49

• 2

• 1

• -2

• -1

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Poll

My level of understanding

(left to right) NO: I don't get it at all, Whoops: need some help but I'm starting to understand, Nailed It: I can do this on my own.