6.7 Calculations with Exponents of Ten
Multiplication and division
In order to clarify the use of some of the exponent rules that we went through on page 6.5, we will calculate with exponents of ten. We will use the first two exponent rules which are useful when calculating exponents of ten.
Exponents with the same base which are to be multiplied together.
a^{b} · a^{c} = a^{b+c}
Example 1
10^{2} · 10^{5} = 10^{2+5} = 10^{7}
Example 2
0.001 · 0.0001= 10^{3} · 10^{4} = 10^{3+(4)} = 10^{7}
Exponents with the same base which are divided by each other.
a^{b}
a^{c} 
= 
a^{bc} 
Example 1
10^{11}
10^{4} 
= 
10^{114}= 10^{7} 
Example 2
0.01
0.00001 
= 
10^{2}
10^{5} 
= 
10^{2(5)}= 10^{3} 
Addition and subtraction
When adding and subtracting powers of ten, we CANNOT use the rules above. The simple way to solve these exercises is to rewrite the powers of ten to normal number before they are calculated.
Exponents with the same base added to each other.
Example
10^{4} + 10^{5} = 10,000 + 100,000 = 110,000
Exponents with the same base subtracted by each other.
Example
10^{3}  10^{2} = 1,000  100 = 900
