Question

Apply the Property of Negative Integer Exponents to generate an expression equivalent to 5^−9/4^−12

with positive exponents only.

Answer 1

[AI-generated answer — Bot GPT 3.5]

To convert the expression 5^(-9)/4^(-12) to an expression with positive exponents only, we can apply the property of negative integer exponents:

a^(-n) = 1/a^n

Using this property, we can rewrite the given expression as:

5^(-9) / 4^(-12) = 1 / (5^9 * 4^12)

Therefore, the equivalent expression with positive exponents only is 1 / (5^9 * 4^12).

Answer 2

are you sure

Answer 3

[AI-generated answer — Bot GPT 3.5]

Apologies for the incorrect response. Let's revise the answer.

To apply the property of negative exponents, we have:

5^(-9) / 4^(-12)

Using the property a^(-n) = 1 / a^n, we can rewrite the expression as:

1 / (5^(9)) / (4^(12))

Now, to further simplify the expression, we can apply another exponent property:

a^(m/n) = (m-th root of a)^n

Let's apply this property to both the numerator and denominator:

1 / ( (5^(9/4)) / (4^(12/4)) )

Simplifying the exponents, we get:

1 / ( (5^(9/4)) / (4^3) )

So, the expression equivalent to 5^(-9) / 4^(-12) with positive exponents only is:

1 / ( (5^(9/4)) / (4^3) )

Answer 4

thats not right

Answer 5

[AI-generated answer — Bot GPT 3.5]

Apologies for the confusion. Let's correct the answer.

To apply the property of negative exponents, we have:

5^(-9) / 4^(-12)

Using the property (a^m) / (a^n) = a^(m-n), we can rewrite the expression as:

(4^12) / (5^9)

Now, let's simplify the expression further:

(2^2)^12 / (5^9)

Applying the property (a^m)^n = a^(m*n), we can simplify further:

2^24 / 5^9

Therefore, the expression equivalent to 5^(-9) / 4^(-12) with positive exponents only is:

2^24 / 5^9

Answer 6

wrong

Answer 7

[AI-generated answer — Bot GPT 3.5]

Apologies for the confusion. Let's correct the answer.

To apply the property of negative exponents, we have:

5^(-9) / 4^(-12)

Using the property a^(-n) = 1 / a^n, we can rewrite the expression as:

1 / (5^(9)) / (4^(12))

Now, to further simplify the expression, we can apply another exponent property:

(a^m) / (a^n) = a^(m-n)

Let's apply this property to simplify the expression:

1 / (5^(9)) / (4^(12)) = 1 / ((5^9) / (4^12))

To apply negative exponent property to both the numerator and denominator, we have:

1 / ( (1 / 5^9) / (1 / 4^12) )

Simplifying the expression, we can multiply the numerator and denominator by the reciprocal of the denominator:

1 / ( (5^9) / (4^12) ) = 1 * (4^12 / 5^9)

Therefore, the expression equivalent to 5^(-9) / 4^(-12) with positive exponents only is:

4^12 / 5^9