Use Properties of Integers and Exponents

Properties of Integer Exponents

Standard: Given a numeric expression with common rational number bases and integer exponents, apply the properties of exponents to generate equivalent expressions.

​Product of Powers Property

​When multiplying two powers with the same base we add the exponents

​

​a^m x aⁿ = a^m+n

​

​a^m(aⁿ) = a^m+n

Multiple Choice

When multiplying two powers with the same base we _______

• add the bases 

• add the exponents 

• multiply the bases 

• multiply the exponents 

Multiple Choice

$$5\left(5^3\right)$$  

What are the two exponents in the problem above

• 5 and 3

• 0 and 5

• 1 and 3

• 1 and 5

Multiple Choice

Simplify the expression  $$5\left(5^3\right)$$  

• $$5^4$$  

• $$5^3$$  

• $$5^2$$  

• 5

​Zero Exponent Property

Any number raised to the zero power is 1.

​

​a⁰ = 1

​

Poll

Select ALL the expressions below that will simplify to 1 

• $$\left(-5\right)^0$$  

• $$\left(-3.6^0\right)$$  

• $$-\ \left(4^0\right)$$  

• $$-\left(7.42^0\right)$$  

Multiple Choice

True or False:  $$b^0=1\$$  

• True 

• False 

​Quotient of Power Property

​When dividing eponential expressions with the same base we subtract the exponents

 

Multiple Choice

When dividing two exponential expressions with the same base you should ____________ the exponents

• add

• subtract

• multiply

• divide

Multiple Choice

Rewrite $$5\left(\frac{1}{5^3}\right)$$   as a division sentence

• $$\frac{5}{5^3}$$  

• $$\frac{5}{5^{-3}}$$  

• Cannont be done

Multiple Choice

Simplify  $$5\left(\frac{1}{5^3}\right)$$   

• $$5^{-2}$$  

• $$5^2$$  

• 5

​Negative Exponent Property

​The negative exponent becomes positive once it is moved

Multiple Choice

Rewrite  $$5^{-3}$$  with a positive exponent.

• $$\frac{1}{5^3}$$  

• $$5^3$$  

• 1