To generate equivalent expressions with only positive exponents, we can apply the following properties of integer exponents:
1. a^m ⋅ a^n = a^(m+n)
2. (a^m)^n = a^(m*n)
3. a^(-n) = 1/a^n
Using these properties, we can simplify the expression:
(4^3 ⋅ 7^(-2))^(-5) / (7^9 ⋅ 4^(-13))
= (4^3)^(-5) / (7^(-2))^(-5) ⋅ (7^9)^(-1) ⋅ (4^(-13))^(-1)
= 4^(-15) / 7^10 ⋅ 7^(-9) ⋅ 4^13
= 4^(-15) ⋅ 7^(-9) ⋅ 4^13 / 7^10
Now, using property 1, we can simplify further:
= 4^(-15 + 13) ⋅ 7^(-9 - 10)
= 4^(-2) ⋅ 7^(-19)
Now, let's convert the expression into a simplified fraction:
= 1/(4^2) ⋅ 1/(7^19)
= 1/16 ⋅ 1/(7^19)
Therefore, the simplified fraction representation of the expression is 1/(16 ⋅ 7^19).
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