Properties of Exponents

Properties of Exponents

Learn and practice

Multiply Properties

• Product of Powers

• Power of a Power

• Power of a Product

Product of Powers

Words: when multiplying like bases, add the exponents

Symbols: (x^a)(x^b) = x^a+b

Numbers: (8³)(8⁶) = 8⁹

Power of a Power

Words: when a power (base with exponent) is raised to another power (exponent), you multiply the exponents (keep the base!)

Symbols: (x^a)^b= x^ab

Numbers: (8³)⁶=8¹⁸

Power of a Product

Words: if two or more bases are grouped together in parentheses and raised to an exponent, each base is raised to that exponent.
Symbols:  $\left(xy\right)^2=x^2y^2$  

Numbers:

 $\left(4abc\right)^3=64a^3b^3c^3$  

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.

Multiple Choice

(2m³)(3m⁴) =

• 5m⁷

• 6m¹²

• 5m¹²

• 6m⁷

Division Properties

• Quotient of Powers

• Power of a Quotient

• Zero Exponent

Quotient of Powers

Words: when dividing like bases, subtract the exponents
Symbols:

 $\frac{x^a}{x^b}=x^{a-b}$  
Numbers:   $\frac{7^7}{7^2}=7^5$  

Power of a Quotient

 

Words: if a fraction is raised to an exponent, both the numerator and denominator are raised to that exponent
Symbols:   $\left(\frac{x}{y}\right)^3=\frac{x^3}{y^3}$  

Numbers:   $\left(\frac{10}{11}\right)^5=\frac{10^5}{11^5}$  

Zero Exponent

Words: any number (except zero) raised to a power of zero is equal to 1
Symbols:   $n^0=1$  

Numbers:   $\left(-8\right)^0=1$  

Multiple Choice

Simplify:

 $\frac{5^7}{5^4}$  

•  $5^{11}$  

•  $1^3$  

•  $5^3$