Exponents Intro

​Exponential Form

• ​Exponential Form is a number made up of two pieces:

  • ​The base is the big, bottom number.

  • ​The exponent is the little number in the top right.

Multiple Choice

What is the base?

$$5^2=25$$  

• 5

• 2

• 25

Multiple Choice

What is the exponent?

$$2^3=8$$  

• 2

• 3

• 8

​What does an exponent mean?

​The exponent tells us how many times to multiply the base by itself.

Multiple Choice

Write the following in expanded form:

$$5^2\ =$$  

• $$5\times2$$  

• $$5\times5$$  

• $$2\times2\times2\times2\times2$$  

• $$5+5$$  

Multiple Choice

Write the following in expanded form:

$$8^4\ =$$  

• $$8\times4$$  

• $$8\times8\times8\times8$$  

• $$4\times4\times4\times4\times4\times4\times4\times4$$  

• $$8+8+8+8$$  

Multiple Choice

Write the following in expanded form:

$$x^3=$$  

• $$x\cdot3$$  

• $$x\cdot x\cdot x$$  

• $$x+3$$  

• $$x+x+x$$  

Multiple Choice

Write the following in exponential form:

$$4\times4\times4\times4\times4=$$  

• $$4\times5$$  

• $$4^5$$  

• $$5^4$$  

Multiple Choice

Write the following in exponential form:

$$11\cdot11\cdot11=$$  

• $$11\times3$$  

• $$11^3$$  

• $$3^{11}$$  

Multiple Choice

Write the following in exponential form:

$$a\cdot a\cdot a=$$  

• $$a\times3$$  

• $$a^3$$  

• $$3^a$$  

Multiple Choice

$$5^2=$$  

• 10

• 52

• 25

• 32

Multiple Choice

$$3^3=$$  

• 9

• 12

• 27

• 6

Multiple Choice

Solve and Simplify (no exponent)

$$2^0$$  

• $$0$$  

• $$1$$  

• $$2$$  

• $$\frac{1}{2}$$  

Multiple Choice

Anything raised to a power of zero is always: 

• 0
• 1
• itself
• negative

Multiple Choice

n⁰ =

• 1

• 0

Multiple Choice

13⁰

• 1
• 2
• 3
• 4

Multiple Choice

Which is greater,  2654⁰ or 5⁰?

• 2654⁰
• 5⁰
• They are the same
• Zero is greater

Multiple Choice

(34x⁵y⁶z^-7)⁰

• 34x⁵y⁶ / z⁷
• 34x⁵y⁶ / x^-7
• 0
• 1

Characteristics of Rational Numbers

• Can be expressed as a fraction

• Represent an exact amount

• Include terminating and repeating decimals

• Include roots of perfect squares and perfect cubes

Characteristics of Irrational numbers

• Cannot be expressed as a fraction

• Represents an approximation

• Decimal form is always non-repeating and non-terminating

• Includes roots of non-perfect square and cube roots

Multiple Choice

Which is an example of an irrational number?

• A non-perfect square
• A fraction
• A whole number
• A perfect square

Multiple Choice

Which of the following numbers is irrational?

• √8
• ¾
• 2
• -1.325

Multiple Choice

√144

• 10
• 11
• 12
• 13

Multiple Choice

√140 is between

• 8 and 9
• 7 and 8
• 7 and 10

• 11 and 12

Multiple Choice

Select the expression that is equal to $$5^3\times5^6$$

• $$5^{3+6}$$

• $$5^3+5^6$$

• $$5^{3\times6}$$

Multiple Choice

Select the expression that is equal to $$x^5\times x^8\times x$$

• $$x^{5+8+1}$$

• $$x^{5\times8\times1}$$

Multiple Choice

Simplify: 3⁵ x 3⁷

• 3¹²

• 9¹²

• 3³⁵

• 9³⁵

Multiple Choice

Select the expression that is equal to $$7^9\div7^2$$

• $$7^{9-2}$$

• $$7^{9\div2}$$

• $$7^{9+2}$$

Multiple Choice

Select the expression that is equal to $$\frac{t^7}{t^3}$$

• $$t^{7-3}$$

• $$t^{7\div3}$$

Multiple Choice

Simplify: 2⁸ ÷ 2²

• 2⁶

• 2⁴

• 2¹⁰

• 1

Multiple Choice

$$\left(2^4\right)^3=$$  

• $$8^3$$  

• $$2^7$$  

• $$2^{12}$$  

• $$8^{12}$$  

Multiple Choice

$$-3^2\times3^0=$$  

• $$6$$  

• $$-6$$  

• $$9$$  

• $$-9$$