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)

Question

What is the solution

Answer 1

First, apply the property of exponents that states (a^n)^m = a^(n*m) to simplify the expression:

(4^3 ⋅ 7^(-2))^(-5) / 7^9 ⋅ 4^(-13)
= (4^15 ⋅ 7^(-10)) / 7^9 ⋅ 4^(-13)
= 4^15 ⋅ 7^(-10) / 7^9 ⋅ 4^(-13)

Next, apply the property of exponents that states a^m / a^n = a^(m-n):

= 4^(15-13) ⋅ 7^(-10-9)
= 4^2 ⋅ 7^(-19)

Now, rewrite 7^(-19) as 1 / 7^19:

= 16 / 7^19

Therefore, the solution is 16 / 7^19.

Answer 2

bot that's wrong

Answer 3

I apologize for the mistake. Let's correct it:

To generate equivalent expressions with only positive exponents, we can use the property of integer exponents:

(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)

Now, rewrite the expression with positive exponents using the property a^(-n) = 1/a^n:

= 1/4^15 ⋅ 7^10 / 7^9 ⋅ 1/4^13
= 1/(4^15 * 4^13) * (7^10 / 7^9)
= 1/4^28 * 7

Therefore, the simplified expression is 1/4^28 * 7. Let's further simplify it:

1/4^28 * 7
= 1/(4^28) * 7
= 7 / 4^28

So, the solution is 7 / 4^28.

Answer 4

that's still wrong

Answer 5

I apologize for the mistake. Let's correct it:

To generate equivalent expressions with only positive exponents, we can use the properties of integer exponents:

(4^3 ⋅ 7^(-2))^(-5) / 7^9 ⋅ 4^(-13)
= 4^(-15) ⋅ 7^(10) / 7^9 ⋅ 4^(-13)
= 1 / (4^15) ⋅ 7^10 / 7^9 ⋅ 1 / 4^13
= 7 / (4^2 * 7) * 1 / (7^9 * 4^13)
= 7 / (16 * 7) * 1 / (7^9 * 4^13)
= 1 / 16 * 1 / (7^9 * 4^13)
= 1 / 16 * 1 / (7^9 * 2^26)
= 1 / (16 * 7^9 * 2^26)
= 1 / (2^4 * 7^9 * 2^26)
= 1 / (2^30 * 7^9).

Therefore, the simplified fraction with no remaining exponents is 1 / (2^30 * 7^9).

Answer 6

bot that's still not right

Answer 7

I apologize for the mistakes in my previous responses. Let's correct it:

To generate equivalent expressions with only positive exponents, we can use the properties of integer exponents:

(4^3 ⋅ 7^(-2))^(-5) / 7^9 ⋅ 4^(-13)
= 4^(-15) ⋅ 7^(10) / 7^9 ⋅ 4^(-13)
= 1 / (4^15) ⋅ 7^10 / 7^9 ⋅ 1 / 4^13
= 7^10 / (4^15 * 7^9) / 4^13
= 7^10 / (4^15 * 7^9 * 4^13)

Now let's simplify the expression further:

= 7^10 / (4^28 * 7^9)
= 1 / (4^28 * 7^(-9) ) * 7^10
= 1 / (4^28 / 7^9) * 7^10
= 1 / ( (2^2)^28 / 7^9 ) * 7^10
= 1 / (2^56 / 7^9) * 7^10
= 1 / (2^56 / 7^9) * 7^10
= 1 / ( 2^56 / 7^9 ) * 7^10
= 1 / (2^56 / 7^9) * 7^10
= 1 / (2^56 / 7^9) * 7^10
= 1 / (2^56 / 7^9) * 7^10
= 7^10 / 2^56 * 7^9
= 7^19 / 2^56.

Therefore, the simplified fraction with no remaining exponents is 7^19 / 2^56.

Answer 8

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)
SIMPLIFY

Answer 9

To simplify the expression and write it with only positive exponents:

First, apply the property of exponents that states (a^m)^n = a^(m*n):

(4^3 ⋅ 7^(-2))^(-5) = 4^(-15) ⋅ 7^(10)

Next, rewrite the expression with positive exponents:

4^(-15) ⋅ 7^(10) / 7^9 ⋅ 4^(-13)
= 1/4^15 ⋅ 7^10 / 7^9 ⋅ 1/4^13
= 7^10 / 4^15 ⋅ 1 / 7^9 ⋅ 1 / 4^13
= 7^10 / 4^15 ⋅ 1 / 7^9 ⋅ 1 / 4^13
= 7^10 / 4^28 ⋅ 1 / 7^9
= 7^10 / 4^28 / 7^9
= 7^10 / 4^28 ⋅ 7^-9
= 7^(10-9) / 4^28
= 7 / 4^28.

Therefore, the simplified expression with only positive exponents is 7 / 4^28.