To simplify the given expression using exponent rules, we need to understand the rules for multiplying and dividing numbers with exponents.
First, let's rewrite the expression with the exponents clearly indicated:
\(7^4 \times 7^3 \times 7^3 \times 7^{-20}\)
Using the multiplication rule of exponents, when multiplying numbers with the same base, we add the exponents. So, applying this rule, we get:
\(7^{4+3+3} \times 7^{-20}\)
Simplifying further gives:
\(7^{10} \times 7^{-20}\)
Using the division rule of exponents, which states that when dividing numbers with the same base, we subtract the exponents, we can rewrite the expression as:
\(7^{10-20}\)
Finally, subtracting the exponents gives us:
\(7^{-10}\)
Therefore, the simplified form of the expression \(74 \times 7 \times 713 \times 7^{-20}\) is \(7^{-10}\).