Question

Apply the Properties of Integer Exponents to generate equivalent expressions to 37⋅3−9 with only positive exponents, then solve the expression. Your answer will be a simplified fraction with no remaining exponents

Answer 1

[AI-generated answer — Bot GPT 3.5]

First, let's rewrite the expression 37⋅3−9 using the properties of integer exponents:

37⋅3−9 = 3^7 ⋅ 3^(-9)

According to the property of multiplying powers with the same base, we can add the exponents:

3^7 ⋅ 3^(-9) = 3^(7+(-9))

Now, let's simplify the sum of the exponents:

7+(-9) = -2

Therefore, the expression is equivalent to:

37⋅3−9 = 3^(-2)

To solve the expression, we need to write it as a fraction with positive exponents:

3^(-2) = 1/3^2

Simplifying the fraction:

1/3^2 = 1/9

So the final answer is 1/9.

Answer 2

how are babies made?

Answer 3

[AI-generated answer — Bot GPT 3.5]

Babies are typically made through a process called sexual reproduction. It involves the coming together of a sperm cell from the male and an egg cell from the female. During sexual intercourse, sperm is ejaculated into the . The sperm then travels through the cervix and uterus and into the fallopian tubes. If there is an egg present in the fallopian tube, fertilization may occur. Fertilization is the fusion of the sperm and egg, resulting in the formation of a zygote. The zygote then undergoes cell division and development, eventually forming an embryo and later a fetus. The fetus continues to develop in the uterus until it is ready to be born as a baby. It's important to note that there are alternative ways to have children, such as through assisted reproductive technologies or adoption.

Answer 4

....

Answer 5

[AI-generated answer — Bot GPT 3.5]

I apologize if my previous response was not what you were expecting or if it did not provide enough information. If you have any specific questions or would like more details on any aspect of reproductive processes, please let me know and I will do my best to provide accurate and informative answers.

Answer 6

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)

Answer 7

[AI-generated answer — Bot GPT 3.5]

Let's apply the Properties of Integer Exponents to generate equivalent expressions for the given expression.

(4^3 ⋅ 7^−2)−5^/7^9 ⋅ 4^−13

Using the property of multiplying powers with the same base, we can rewrite (4^3 ⋅ 7^−2) as 4^3 ⋅ 7^−2.

Using the property of dividing powers with the same base, we can rewrite 5^/7^9 as 5^7/7^9.

Therefore, the expression becomes:

(4^3 ⋅ 7^−2)/(5^7/7^9) ⋅ 4^−13

Now let's simplify the expression by applying the rules of exponents:

(4^3 ⋅ 7^−2)/(5^7/7^9) ⋅ 4^−13

Using the rule a^m/n = (n√a)^m:

(4^(3/1) ⋅ 7^(-2/1))/(5^(7/1) ⋅ 7^(9/1)) ⋅ 4^(-13/1)

Simplifying the exponents:

4^3 ⋅ 7^(-2)/(5^7 ⋅ 7^9) ⋅ 4^(-13)

Now, let's combine the like terms using the rule a^m ⋅ a^n = a^(m+n):

(4^3 ⋅ 7^(-2) ⋅ 4^(-13))/(5^7 ⋅ 7^9)

Applying the rule of subtracting exponents in the denominator:

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

Simplifying the exponents:

(4^3 ⋅ 7^(-2) ⋅ 4^(-13))/(5^7 ⋅ 7^2)

Since we want to express everything with positive exponents, let's apply the rule a^(-n) = 1/(a^n):

(4^3 ⋅ 1/(7^2) ⋅ 1/(4^13))/(5^7 ⋅ 7^2)

Simplifying the expression:

(4^3)/(7^2 ⋅ 5^7 ⋅ 4^13)

Now, let's combine the powers using the rule a^m ⋅ b^m = (a⋅b)^m:

((4⋅4⋅4)/(7⋅7))/(5^7 ⋅ 4^13)

Simplifying further:

64/(49 ⋅ 4)/(5^7 ⋅ 4^13)

Now, let's express 4 as 2^2:

64/(49 ⋅ 2^2)/(5^7 ⋅ 2^13)

Simplifying:

64/(49 ⋅ 4)/(5^7 ⋅ 2^13)

Now, let's express 49 as 7^2:

64/(7^2 ⋅ 4)/(5^7 ⋅ 2^13)

Simplifying:

64/(7^2 ⋅ 4)/(5^7 ⋅ 2^13)

Now, let's simplify the expression inside the parentheses and combine like terms:

64/(49 ⋅ 4)/(2^13 ⋅ 5^7)

64/(196)/(8192 ⋅ 5^7)

Now, let's simplify further:

64/(196)/(8192 ⋅ 78125)

Now, let's divide 64 by 196:

1/(3)/(8192 ⋅ 78125)

Now, let's multiply 8192 and 78125:

1/(236,421,120)

So, the simplified fraction with no remaining exponents is 1/236,421,120.

Answer 8

Apply the Properties of Integer Exponents to generate equivalent expressions to 3^7⋅3^−9 with only positive exponents, then solve the expression. Your answer will be a simplified fraction with no remaining exponents

Answer 9

Apply the Properties of Integer Exponents to generate equivalent expressions 2^2/2-^4

Answer 10

[AI-generated answer — Explain Bot]

To apply the properties of integer exponents and generate equivalent expressions with positive exponents for 37⋅3−9, we can follow these steps:

Step 1: Express 37 as a power of 3:
37 = 3^1⋅3^6

Step 2: Apply the property of multiplying exponents with the same base:
37 = 3^(1+6)
= 3^7

Step 3: Rewrite 3^(-9) using the reciprocal property:
3^(-9) = 1 / 3^9

Now we can substitute these equivalent expressions into the original expression:

37⋅3^(-9) = 3^7 ⋅ (1 / 3^9)

Step 4: Apply the property of dividing exponents with the same base:
3^7 / 3^9 = 3^(7-9)
= 3^(-2)

Step 5: Rewrite 3^(-2) using the reciprocal property:
3^(-2) = 1 / 3^2

Finally, simplifying the expression:

37⋅3^(-9) = 3^7 ⋅ (1 / 3^9)
= 3^(-2)
= 1 / 3^2
= 1 / 9

Therefore, the simplified fraction with no remaining exponents for 37⋅3^(-9) is 1/9.