Question

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.

Answer 1

that is inncorrect 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.

Answer 2

Which of the following is an equivalent expression to 5^9⋅5^−13 with only positive exponents that has been generated by applying the Properties of Integer Exponents?(1 point)

Answer 3

To apply the properties of integer exponents, we can use the following rules:

1. (a^m)^n = a^(m*n)
2. a^(-n) = 1/a^n
3. a^0 = 1
4. a^1 = a
5. a^m/a^n = a^(m-n)

First, let's simplify the expression using the properties of integer exponents:

(4^3 ⋅ 7^(-2))^(-5)/(7^9 ⋅ 4^(-13))

Using rule 1, we can simplify the expression inside the parentheses:

4^(3*(-5)) ⋅ 7^((-2)*(-5))/(7^9 ⋅ 4^(-13))

This becomes:

4^(-15) ⋅ 7^10/(7^9 ⋅ 4^(-13))

Using rule 2, we can convert the negative exponents to positive exponents:

1/4^15 ⋅ 7^10/(7^9 ⋅ 4^(-13))

Using rule 5, we can simplify the expression further:

1/(4^15 ⋅ 4^(-13) ⋅ 7^(-9) ⋅ 7^10)

Using rule 1, we can combine the exponents with the same base:

1/(4^(15 + (-13)) ⋅ 7^(-9 + 10))

Simplifying the exponent calculations:

1/(4^2 ⋅ 7^1)

Using rule 4 and simplifying further:

1/(16 ⋅ 7)

Simplifying the expression:

1/112

Therefore, the simplified fraction is 1/112.