Introduction to Exponents

Introduction to Exponents

​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

Multiple Choice

What is the base?

$$x^4$$  

• x

• 4

• There is no base.

​What does an exponent mean?

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

​More examples...

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:

$$3^5\ =$$  

• $$3\cdot5$$  

• $$3\cdot3\cdot3\cdot3\cdot3$$  

• $$5\cdot5\cdot5$$  

• $$3+3+3+3+3$$  

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:

$$a\cdot a\cdot a=$$  

• $$a\times3$$  

• $$a^3$$  

• $$3^a$$  

​Solving with an exponent

​When solving for the final answer, take it step by step, multiplying two values at a time.

Multiple Choice

$$5^2=$$  

• 10

• 52

• 25

• 32

Multiple Choice

$$3^3=$$  

• 9

• 12

• 27

• 6

Fill in the Blank

$$10^3=$$  

Fill in the Blank

$$4^3=$$  

​10s Trick!!

When the base is 10, look at ​exponent, and that is how many zeros are in the answer!

Multiple Choice

How many zeros will be in the answer to  $$10^6$$  ?

• 10

• 6

• 16

• 60

• You can't tell.

Multiple Choice

Solve:  $$10^4$$  

• 10,000,000,000

• $$10,000$$  

• 40

• 1,000

• 100,000