To determine which expression is equivalent to [tex]\(10 \times 10^4 \times 10^3 \times 10^{-5}\)[/tex], let's go through the problem step by step, applying the properties of exponents.
### Step 1: Identify the base
The base for all the exponential terms is 10.
### Step 2: Simplify the expression using exponent rules
The expression given is:
[tex]\[
10 \times 10^4 \times 10^3 \times 10^{-5}
\][/tex]
### Step 3: Apply the exponent addition rule
When multiplying numbers with the same base, you add their exponents. For a base [tex]\(10\)[/tex], we can simplify the multiplication as follows:
[tex]\[
10^1 \times 10^4 \times 10^3 \times 10^{-5}
\][/tex]
The exponents can be added together:
[tex]\[
1 + 4 + 3 + (-5)
\][/tex]
### Step 4: Calculate the sum of exponents
Perform the addition within the exponents:
[tex]\[
1 + 4 + 3 + (-5) = 1 + 4 + 3 - 5 = 8 - 5 = 3
\][/tex]
### Step 5: Write the equivalent exponential expression
After summing the exponents, we get:
[tex]\[
10^{3}
\][/tex]
So, the expression [tex]\(10 \times 10^4 \times 10^3 \times 10^{-5}\)[/tex] is equivalent to [tex]\(10^{3}\)[/tex].
Thus, the correct answer is:
[tex]\[
\boxed{10^3}
\][/tex]
