Multiplication Property of Exponents
We can extend the Multiplication Property of Exponents to multiply more
than two factors.
Example 1
Find: 8^{4} Â· 8
Â· 8^{5}. Leave your answer in exponential notation.
Solution
The bases are the same, so we can use the
Multiplication Property of Exponents.
Note: 8 = 8^{1}
8^{4} Â· 8
Â· 8^{5} = 8^{4}
Â· 8^{1}
Â· 8^{5} = 8^{4 + 1 + 5} = 8^{10}
We left 8^{10} in exponential form. To
evaluate 8^{10}, use the â€œy^{x}â€ key on a
scientific calculator or the â€œ^â€ key
on a graphing calculator.
8^{10 }= 1,073,741,824
Example 2
Find: x^{7} Â· x^{3}
Â· x^{5}
Solution
The operation is multiplication and
the bases are the same.
Therefore, add the exponents and use x as the base. x^{7}
Â· x^{3}
Â· x^{5} = x^{7 + 3 + 5} = x^{15 }
