To apply the properties of integer exponents, we can use the rules:
1) (a^m)^n = a^(m*n)
2) a^(-n) = 1/a^n
3) (a/b)^n = (a^n)/(b^n)
Using these rules, we can simplify the expression as follows:
(4^3 * 7^-2)^-5 / 7^9 * 4^-13
= (4^(3*-5) * 7^(-2*-5)) / (7^9 * 4^-13)
= (4^-15 * 7^10) / (7^9 * 4^-13)
= (7^10 / 4^15) / (7^9 / 4^13)
= (7^10 / 7^9) * (4^13 / 4^15)
= 7^(10-9) * 4^(13-15)
= 7^1 * 4^-2
= 7/4^2
= 7/16
Therefore, the simplified fraction is 7/16.
Apply the Properties of Integer Exponents to generate equivalent expressions to (4^3 ⋅ 7^−2)^−5 / 7^9 ⋅ 4^−13 with only positive exponents, then solve the expression. Your answer will be a simplified fraction with no remaining exponents.(1 point)
(4^3 ⋅ 7^−2)−5 / 7^9 ⋅ 4^−13=
1 answer