apply the Properties of Integer Exponents to generate an equivalent expression to (5−3)6⋅ 51710−2 (1 point) Responses 500 500 20 20 1500 1 over 500 120 1 over 20
To simplify the given expression using the properties of integer exponents, we first need to write the expression more clearly:
(5^(-3))^6 * 5^(17*10^(-2))
Let's apply the properties of exponents step by step:
1. Power of a power: (a^m)^n = a^(m*n)
(5^(-3))^6 = 5^(-3*6) = 5^(-18)
2. Multiplication of exponents with the same base: a^m * a^n = a^(m + n)
Since 17*10^(-2) is equivalent to 17*(1/100) = 17/100 = 0.17, we can now express the second part of the expression:
5^(17*10^(-2)) = 5^0.17
Now the entire expression looks like this:
5^(-18) * 5^0.17
Apply the multiplication property of exponents with the same base:
5^(-18 + 0.17) = 5^(-17.83)
The simplified expression is 5^(-17.83). However, none of the provided responses seems to match this result directly. If you're sure about the original expression and the responses, there might be a mistake or misinterpretation. If you're looking for positive integer exponents, you would need to revisit the problem and confirm the values given are indeed correct.