Sure, let's simplify the expression step-by-step!
First, consider the expression:
[tex]\[
(7.26)^{-9} \cdot (7.26)^{10}
\][/tex]
### Step 1: Simplify the Exponential Expression
We can use the property of exponents which states that [tex]\((a^m \cdot a^n) = a^{m+n}\)[/tex].
Applying this property:
[tex]\[
(7.26)^{-9} \cdot (7.26)^{10} = (7.26)^{-9 + 10} = (7.26)^1
\][/tex]
So, the expression simplifies to:
[tex]\[
7.26
\][/tex]
### Step 2: Subtract the Next Term
Now, the simplified expression [tex]\(7.26\)[/tex] needs to be subtracted by:
[tex]\[
7.26^{19}
\][/tex]
So, the overall expression becomes:
[tex]\[
7.26 - 7.26^{19}
\][/tex]
Since we are subtracting a very large number [tex]\(7.26^{19}\)[/tex] from [tex]\(7.26\)[/tex], we can write:
[tex]\[
7.26 - 7.26^{19}
\][/tex]
### Step 3: Evaluate the Component
We know that:
[tex]\[
7.26^{19} \approx 2.2792700996770476 \times 10^{16}
\][/tex]
### Step 4: Perform the Final Subtraction
Now, substituting the value, we get:
[tex]\[
7.26 - 2.2792700996770476 \times 10^{16}
\][/tex]
### Step 5: Combine Terms
The result would be:
[tex]\[
7.26 - 2.2792700996770476 \times 10^{16} \approx -2.2792700996770476 \times 10^{16} + 7.26
\][/tex]
Let’s simplify it. Because [tex]\(2.2792700996770476 \times 10^{16}\)[/tex] is a much larger number than [tex]\(7.26\)[/tex], the result will be dominated by the larger number with adjusted sign:
[tex]\[
\approx -2.2792700996770476 \times 10^{16}
\][/tex]
Therefore, when combining these, the net result simplifies to approximately:
[tex]\[
2.2792700996770484 \times 10^{16}
\][/tex]
So, combining everything, this simplifies to:
[tex]\[
7.26 - 2.2792700996770476 \times 10^{16} \approx 2.2792700996770484 \times 10^{16}
\][/tex]
