Simplifying Exponent Expressions

The problem requires simplifying the expression $57^{-8} \div 57^{17} \times 57^{-18}$ using the rules of exponents.

Solution Steps

• Recall the exponent rules:
  • Division: $a^m \div a^n = a^{m-n}$
  • Multiplication: $a^m \times a^n = a^{m+n}$
• Apply the division rule to the first part of the expression: $57^{-8} \div 57^{17} = 57^{-8 - 17} = 57^{-25}$
• Now, multiply the result by the next term, $57^{-18}$: $57^{-25} \times 57^{-18}$
• Apply the multiplication rule: $57^{-25 + (-18)} = 57^{-25 - 18} = 57^{-43}$

The simplified value of the expression is $57^{-43}$.