Question
Choose the correct simplification of the expression [tex]f^{4} * f^{8}[/tex]
Answer:
[tex]f^{4} * f^{8}[/tex] = [tex]f^{12}[/tex]
Step-by-step explanation:
Topic: Indices
There are two methods of doing this;
Method 1
[tex]f^{4} * f^{8}[/tex] ----- Expand both indices
= [tex](f * f * f * f) * (f * f * f * f * f * f * f * f)[/tex] -- The total number of f is 12, so we have
= [tex]f^{12}[/tex]
So, [tex]f^{4} * f^{8} = f^{12}[/tex]
This method is not advisable when dealing with a large indices; hence, the need for method 2.
Method 2
Applying law of indices;
The first law of indices
The first law of indices states: [tex]a^{m} * a^{n} = a^{m+n}[/tex].
This means that when numbers in index form with the same base are multiplied by each other, the powers (indices) are added together.
Applying this law on [tex]f^{4} * f^{8}[/tex]
[tex]f^{4} * f^{8}[/tex] = [tex]f^{4 + 8}[/tex]
[tex]f^{4} * f^{8}[/tex] = [tex]f^{12}[/tex]
