Apply All Exponent Rules Quick Check

Question

1 of 51 of 5 Items
Question
Which of the following is an equivalent expression to 59⋅5−13 with only positive exponents that has been generated by applying the Properties of Integer Exponents?(1 point)

Answer 1

The expression 59⋅5−13 can be simplified using the rules of exponents:
1. The product rule: a^m * a^n = a^(m+n)
2. The power rule: (a^m)^n = a^(m*n)
3. The quotient rule: a^m / a^n = a^(m-n)

Applying these rules to the expression 59⋅5−13:
59⋅5−13 = (5^9) * (5^-13)

By applying the product rule, we add the exponents:
(5^9) * (5^-13) = 5^(9+(-13))

Simplifying the exponent:
5^(9+(-13)) = 5^(-4)

Therefore, the equivalent expression with only positive exponents is 5^(-4).