To apply the properties of integer exponents, we can rewrite the expression as follows:
(4^3 ⋅ 7^(-2))^(-5) / 7^9 ⋅ 4^(-13)
Now, let's simplify each term using the following rule:
(a^m)^n = a^(m*n)
(4^3 ⋅ 7^(-2))^(-5) = 4^(3*(-5)) ⋅ 7^((-2)*(-5))
Simplifying further:
4^(-15) ⋅ 7^10 / 7^9 ⋅ 4^(-13)
Now, let's simplify the remaining terms using the rule:
a^m/a^n = a^(m-n)
4^(-15) ⋅ (7^10 / 7^9) ⋅ 4^(-13)
Simplifying further:
4^(-15) ⋅ 7^(10-9) ⋅ 4^(-13)
4^(-15) ⋅ 7^1 ⋅ 4^(-13)
Lastly, let's simplify the remaining terms using the rule:
a^m ⋅ a^n = a^(m+n)
4^(-15) ⋅ 7 ⋅ 4^(-13) = 4^((-15)+(-13)) ⋅ 7
4^(-28) ⋅ 7
Finally, the equivalent expression with only positive exponents is:
7/4^28
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