To solve the expression \( r^2 \cdot r \cdot r^5 \), let's follow a step-by-step process:
1. Identify the Problem:
We have the expression \( r^2 \cdot r \cdot r^5 \) to simplify.
2. Recall the Properties of Exponents:
One of the key properties of exponents is that when you are multiplying bases that are the same, you add their exponents.
In mathematical terms:
[tex]\[
a^m \cdot a^n = a^{m+n}
\][/tex]
where \( a \) is the base, and \( m \) and \( n \) are the exponents.
3. Apply the Property to the Given Expression:
Here, \( r \) is the base, and the exponents are 2, 1, and 5 respectively (note that \( r \) can be written as \( r^1 \)).
So, the expression \( r^2 \cdot r \cdot r^5 \) can be simplified by adding the exponents:
[tex]\[
r^2 \cdot r \cdot r^5 = r^{2+1+5}
\][/tex]
4. Simplify the Exponents:
Now, add the exponents together:
[tex]\[
2 + 1 + 5 = 8
\][/tex]
5. Write the Simplified Expression:
Therefore, the simplified expression is:
[tex]\[
r^8
\][/tex]
Thus, the answer is [tex]\( r^8 \)[/tex].
