Of course! Let's simplify the given mathematical expression step-by-step:
Given expression:
[tex]\[
(7.26)^{-9} \cdot (7.26)^{10} - 7.26^{19}
\][/tex]
### Step 1: Simplify the product of terms with the same base using the properties of exponents.
We have:
[tex]\[
(7.26)^{-9} \cdot (7.26)^{10}
\][/tex]
To simplify this, we use the property of exponents that states [tex]\(a^m \cdot a^n = a^{m+n}\)[/tex]. Therefore:
[tex]\[
(7.26)^{-9} \cdot (7.26)^{10} = 7.26^{-9+10} = 7.26^1 = 7.26
\][/tex]
### Step 2: Substitute back into the expression.
Now, the simplified form of [tex]\((7.26)^{-9} \cdot (7.26)^{10}\)[/tex] is [tex]\(7.26\)[/tex]. So, we substitute this back into the original expression:
[tex]\[
7.26 - 7.26^{19}
\][/tex]
### Step 3: Analyze the subtraction.
The expression is already in its simplest form, so we write:
[tex]\[
7.26 - 7.26^{19}
\][/tex]
### Final Result
The simplified form of the given expression is:
[tex]\[
7.26 - 7.26^{19}
\][/tex]
Numerically, this evaluates to approximately:
[tex]\[
7.26 - 2.2792700996770468 \times 10^{16}
\][/tex]
So, the result is approximately:
[tex]\[
(7.26, -2.2792700996770468 \times 10^{16})
\][/tex]
