Multiplying Exponents with the same base

Multiplying Exponents with the same base

Quick Review

•  $n^0\ =\ 1$  
  

• When a number is written without an exponent, it is understood to be an exponent of 1

•  $n^1\ \ =\ n$  

Product of Powers Property

• To multiply powers with the same base, add their exponents.

•  $4^2\ \ x\ \ 4^3\ =\ 4^5\ \ \ \ \$  

•  $a^m\ \ \ \ x\ \ \ \ a^n\ \ \ \ \ =a^{\left(m+n\right)}\$  

Finding the Power of a Power

•  $\left(w^5\right)^4$  

• When finding the power of a power, multiply the exponents

• w^20

Tricky

•  $2n^4\ \times\ 5n^4$  

• multiply the coefficients (the numbers)

• 2 x 5 = 10

• then add the exponents of the same base, n

•  $10n^8$  

Trickier

•  $7v^{3\ }\times\ 10u^3v^5$  

• multiply numbers, 7 x 10 = 70

• add exponents together of the SAME base

•  $v^{3\ }\times\ v^5\ \ =\ v^8$  

•  $70u^3v^8$