Question

pply 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

Answer 1

are you sure

Answer 2

wrong

Answer 3

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

First, let's simplify the expression:
(4^3⋅7^−2) ^−5/7^9 ⋅ 4^−13

Using the property of negative exponents, we can rewrite the expression as:
(4^3/7^2)^-5/7^9 ⋅ 4^(-13)

Now, let's simplify the exponents:
(64/49)^(-5/49) ⋅ (1/4^13)

Using the property of raising a fraction to a negative exponent, we can rewrite the expression as:
(49/64)^(5/49) ⋅ 1/(2^26)

Now, let's simplify the expression further by converting to a single fraction:
(49/64)^(5/49) / (2^26)

Now, let's simplify the exponents:
49^(5/49) / 64^(5/49) / 2^26

Now, let's simplify the base and exponent of 49^(5/49):
7^5 / 64^(5/49) / 2^26

Now, let's simplify the base and exponent of 64^(5/49):
7^5 / 4^(5/7) / 2^26

Finally, let's simplify the base and exponent of 4^(5/7):
7^5 / 2^(5/7) / 2^26

We can combine the exponents of the denominator:
7^5 / 2^(5/7 + 26)

Now, let's simplify the exponent of the denominator:
7^5 / 2^(5/7 + 182/7)

Now, let's simplify the exponent further:
7^5 / 2^(187/7)

Now, let's simplify the expression further by converting the denominator to a fraction with a common denominator:
7^5 / 2^(187/7)

Now, let's convert the denominator to a radical:
7^5 / √(2^187)

Finally, let's simplify the expression further by evaluating the square root and raising it to the 7th power:
7^5 / (2^26 √2)

Therefore, the simplified expression is 7^5 / (2^26 √2).

Answer 4

Apologies for the mistake in my previous response. Here is the correct solution:

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

First, let's simplify the expression:
(4^3⋅7^−2) ^−5/7^9 ⋅ 4^−13

Using the property of negative exponents, we can rewrite the expression as:

(4^3/7^2) ^−5/7^9 ⋅ 1/(4^13)

Now, let's simplify the exponents:
(64/49)^(-5/49) ⋅ 1/(2^52)

Next, we can apply the property of negative exponents to rewrite (64/49)^(-5/49) as (49/64)^(5/49).
This gives us:

(49/64)^(5/49) ⋅ 1/(2^52)

Now, let's simplify further by expressing (49/64)^(5/49) as a radical:

√(49/64)^(5) ⋅ 1/(2^52)

Simplifying the radicals:

(7/8)^5 ⋅ 1/(2^52)

Now, we can simplify the expression by multiplying the exponents:

7^5 / 8^5 ⋅ 1/(2^52)

Finally, we can simplify further by evaluating the exponents:

16807 / 32768 ⋅ 1/(2^52)

Therefore, the simplified expression is 16807/(32768⋅2^52).

Answer 5

Apologies for the confusion. Let's try again:

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

First, let's simplify the expression:
(4^3⋅7^−2) ^−5/7^9 ⋅ 4^−13

Using the property of negative exponents, we can rewrite the expression as:

(4^3/7^2) ^−5/7^9 ⋅ 1/(4^13)

Now, let's simplify the exponents:
(64/49)^(-5/49) ⋅ 1/(2^52)

Using the property of raising a fraction to a negative exponent, we can rewrite the expression as:
(49/64)^(5/49) ⋅ 1/(2^52)

Now, let's simplify the expression further:
49^(5/49)/64^(5/49) ⋅ 1/(2^52)

Since the base and exponent of 49^(5/49) are the same, the exponent simplifies to 1:
49/64^(5/49) ⋅ 1/(2^52)

Since the exponent of 64^(5/49) is also 1, the expression becomes:
49/64 ⋅ 1/(2^52)

Now, let's simplify the expression further:
49/64 ⋅ 1/(2^52)

Now, let's simplify the denominator:
49/64 ⋅ 1/(2^52)

Now, let's simplify the exponent of 2:
49/64 ⋅ 1/(2^(52/1))

Now, let's simplify the exponent further:
49/64 ⋅ 1/(2^52)

Now, let's evaluate the expression:
49/64 ⋅ 1/(4,503,599,627,370,495,609,375)

To simplify the expression, we can multiply the numerator and denominator:
49 / (64 * 4,503,599,627,370,495,609,375)

Finally, let's write the simplified fraction:
49 / 288,230,376,151,711,744,052,585,840,123,873,750

Therefore, the simplified expression is 49 / 288,230,376,151,711,744,052,585,840,123,873,750.