Exponent Rules Power to a Power

Exponent Rules

Apply the Exponent Product Rule and Power to a Power Rule to simplify expressions.

Product Exponent Rule

​

​Simplify the Expression

​When multiplying powers with the same base, add the exponents.


Ex.

Multiple Choice

According to exponent rules, when we multiply two power with the same base we _______ the exponents.
Example: c⁶ ⋅ c⁴

• add
• subtract
• multiply
• divide

Multiple Choice

Anything raised to a power of zero is always: 

• 0
• 1
• itself
• negative

Multiple Choice

To solve

$$6^66^3$$  
you must_________ the exponents

• divide

• add

• subtract

• multiply

Multiple Choice

$$365^0=$$  

• 0

• 1

• 365

• $$\frac{1}{365}$$  

Multiple Choice

Which is equivalent to 5 x 5 x 5 x 5

• 5³
• 5⁴
• 4⁵
• 5⁵

Multiple Choice

Simplify:
b² ⋅ b⁴

• b⁸
• b⁶
• b²
• 2b⁶

Multiple Choice

Which expression is equivalent to $$2^8\cdot2^{10}$$  ?

• $$2^{18}$$  

• $$4^{18}$$  

• $$2^{80}$$  

• $$4^{80}$$  

Multiple Choice

Simplify the following expression:

r⁶ ⋅ r² ⋅ r³

• r⁶²³

• r¹¹

• 11r

• r³⁶

Multiple Choice

$$10^3=$$  

• $$10\times10\times10$$  

• $$10\times3$$  

• $$10+10+10$$  

• 10,000

Multiple Choice

If a number or variable does not have an exponent, we can assume the exponent is:

• 0

• 1

Multiple Choice

Which number is the BASE? $$2^7$$ = 128

• 2

• 7

• 128

• $$2^7$$  

Multiple Choice

Simplify: $$2^3\cdot2^4\cdot3^2$$  

• $$2^{12}\cdot3^2$$  

• $$12^9$$  

• $$2^7\cdot3^2$$  

• $$6^9$$  

Multiple Choice

3³ ⋅ 3

• 3⁴
• 3³
• 3⁰
• 1 ⁄ 3⁴

Multiple Choice

How do you correctly say 4³

• 4 squared

• 3 quadrupled

• 4 cubed

• 4 to the power of 2

Multiple Choice

$$10^{-8}\ \cdot\ 10^{-4}$$  

• $$10^{32}$$  

• $$10^{-32}$$  

• $$10^2$$  

• $$10^{-12}$$  

Multiple Choice

$$2\cdot2^3\cdot2^4$$  Using exponents, simplify the following expression:

• $$2^{12}$$  

• $$2^7$$  
  

• $$2^8$$  
  

• $$2^{12}$$  
  

Multiple Choice

$$7^{15}\ \cdot\ 7^{-20}$$  

• $$7^{-5}$$  

• $$7^{-300}$$  

• $$7^5$$  

• $$7^{300}$$  

Multiple Choice

According to exponent rules, when we raise the power to a power we _______ the exponents.
Example: (d²)⁵

• add
• subtract
• multiply
• divide

Multiple Choice

Simplify the expression: 

$$\left(2^2\right)^4$$  

• $$2^6$$  

• $$2^2$$  

• $$4^8$$  

• $$2^8$$  

Multiple Choice

• x²

• 0

• 1

• x²⁰

Multiple Choice

$$\left(3^5\right)^4$$  

• $$3^9$$  

• $$3^{20}$$  

• $$3^1$$  

Multiple Choice

$$\left(2^3\right)^2$$  

• $$2^6$$  

• $$2^5$$  

• $$6^2$$  

• $$2^1$$  

Multiple Choice

$$\left(2^3\right)^3$$  

• $$2^6$$  

• $$2^9$$  

• $$8^3$$  

• $$6^3$$  

Multiple Choice

$$\left(2^{11}\right)^8$$  

• $$2^{88}$$  

• $$2^{19}$$  

• $$22^8$$  

• $$16^{11}$$  

Multiple Choice

$$\left(3^4\right)^4$$  

• $$3^8$$  

• $$3^{16}$$  

• $$12^4$$  

Multiple Choice

$$\left(28^{-2}\right)^3$$  

• $$28^{-6}$$  

• $$28^1$$  

• $$28^6$$  

• $$28^{\cdot1}$$  

Multiple Choice

$$\left(35^{-9}\right)^{-2}$$  

• $$35^{-18}$$  

• $$35^{18}$$  

• $$35^{-11}$$  

• $$35^{11}$$  

Multiple Choice

• 25⁶⁰
• 25¹⁷
• 5⁶⁰
• 5¹⁷