Certainly! Let's simplify the given expression step-by-step.
You have the expression:
[tex]\[
\frac{a^7}{a^5}
\][/tex]
### Step 1: Understand the properties of exponents
When dividing two expressions with the same base, we subtract the exponent of the denominator from the exponent of the numerator. Mathematically, this rule is expressed as:
[tex]\[
\frac{a^m}{a^n} = a^{m-n}
\][/tex]
### Step 2: Apply the exponent rule to the given expression
Here, the base [tex]\(a\)[/tex] is the same in both the numerator and the denominator. You have [tex]\(a^7\)[/tex] in the numerator and [tex]\(a^5\)[/tex] in the denominator. Using the property of exponents mentioned:
[tex]\[
\frac{a^7}{a^5} = a^{7-5}
\][/tex]
### Step 3: Simplify the exponent
Calculate the exponent in the simplified form:
[tex]\[
a^{7-5} = a^2
\][/tex]
### Step 4: Write the final simplified expression
Thus, the simplified form of [tex]\(\frac{a^7}{a^5}\)[/tex] is:
[tex]\[
a^2
\][/tex]
So, [tex]\(\frac{a^7}{a^5} = a^2\)[/tex].
This completes the simplification process. The final answer is:
[tex]\[
a^2
\][/tex]
