To simplify the expression using exponent rules, we can apply the rule that states when multiplying two numbers with the same base, we add their exponents.
First, let's simplify the exponents:
7^4 × 7 × 7^13 × 7^(-20)
To multiply 7^4 and 7^13, we add their exponents:
7^(4+13) × 7 × 7^(-20)
Now, let's simplify the exponent (4+13):
7^17 × 7 × 7^(-20)
Next, we multiply 7^17 and 7:
7^(17+1) × 7^(-20)
Simplifying the exponent (17+1):
7^18 × 7^(-20)
Finally, to multiply 7^18 and 7^(-20), we add their exponents:
7^(18+(-20))
Simplifying the exponent (18+(-20)):
7^(-2)
Therefore, the simplified expression is 7^(-2).