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.(1 point)
37⋅3−9
37⋅3−9
Answers
Answer
thats is incorrect
Answer
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.(1 point)
3^7⋅3^−9=
3^7⋅3^−9=
Answer
Apply the Properties of Integer Exponents to generate equivalent expressions to 4^0 ⋅ 5^−2/ (−2)^−3 with only positive exponents, then solve the expression. Your answer will be a simplified fraction with no remaining exponents.(1 point)
4^0 ⋅ 5^−2/ (−2)^−3=
4^0 ⋅ 5^−2/ (−2)^−3=
Answer
that is incorrect
Answer
Apply the Properties of Integer Exponents to generate equivalent expressions to (14^3⋅27^−7)^0/ 3^4 with only positive exponents, then solve the expression. Your answer will be a simplified fraction with no remaining exponents.(1 point)
(14^3⋅27^−7)^0/ 3^4=
(14^3⋅27^−7)^0/ 3^4=
Answer
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)
(4^3 ⋅ 7^−2)^−5 /7^9 ⋅ 4^−13=
(4^3 ⋅ 7^−2)^−5 /7^9 ⋅ 4^−13=
Answer
thats wrong
Answer
thats incorrect bot
Answer
who is dd osama bot?
Answer
who is dd osama?
Answer
who is dd osama, his little brother died notti osama at 14, and dd osama is 16 who is he?
Answered by
GPT 3.5
To apply the properties of integer exponents and generate equivalent expressions with positive exponents, we can use the following rules:
1. For any nonzero number a and integer n, a^(-n) is equal to 1/a^n.
2. For any nonzero number a and integers m and n, a^m * a^n is equal to a^(m + n).
Using these rules, we can rewrite 37⋅3^(-9) as:
(1/37) * 3^(-9)
Now, we can simplify this expression further:
(1/37) * 3^(-9) = (1/37) * (1/3^9)
= (1/37) * (1/(3^3)^3)
= (1/37) * (1/27^3)
= 1 / (37 * 27^3)
Finally, we can calculate the value of this expression:
1 / (37 * 27^3) = 1 / (37 * 19683)
= 1 / 727389
= 1/727389.
So, the simplified fraction with no remaining exponents is 1/727389.
1. For any nonzero number a and integer n, a^(-n) is equal to 1/a^n.
2. For any nonzero number a and integers m and n, a^m * a^n is equal to a^(m + n).
Using these rules, we can rewrite 37⋅3^(-9) as:
(1/37) * 3^(-9)
Now, we can simplify this expression further:
(1/37) * 3^(-9) = (1/37) * (1/3^9)
= (1/37) * (1/(3^3)^3)
= (1/37) * (1/27^3)
= 1 / (37 * 27^3)
Finally, we can calculate the value of this expression:
1 / (37 * 27^3) = 1 / (37 * 19683)
= 1 / 727389
= 1/727389.
So, the simplified fraction with no remaining exponents is 1/727389.
Answered by
GPT 3.5
I apologize for the mistake. Let's try again.
To apply the properties of integer exponents, we have:
37 * 3^(-9)
Now, let's rewrite 3^(-9) with positive exponents using the property a^(-n) = 1/a^n:
37 * (1/3^9)
By simplifying 3^9, we have:
37 * (1/19683)
Now, let's multiply the numbers together:
37/19683
So, the equivalent expression with positive exponents is 37/19683.
To apply the properties of integer exponents, we have:
37 * 3^(-9)
Now, let's rewrite 3^(-9) with positive exponents using the property a^(-n) = 1/a^n:
37 * (1/3^9)
By simplifying 3^9, we have:
37 * (1/19683)
Now, let's multiply the numbers together:
37/19683
So, the equivalent expression with positive exponents is 37/19683.
Answered by
GPT 3.5
To generate an equivalent expression with only positive exponents, we can use the property of integer exponents that states: a^m * a^n = a^(m+n).
Using this property, we can rewrite the expression as:
3^7 * 3^(-9) = 3^(7 + (-9))
To simplify the exponent inside the parentheses, we can add the negative exponent:
3^(7 - 9)
Simplifying further, we have:
3^(-2)
Now, we can apply the property of negative exponents, which states that a^(-n) = 1/a^n. In this case, we have:
3^(-2) = 1/3^2
Simplifying the expression, we get:
1/9
Therefore, the equivalent expression with only positive exponents is 1/9.
Using this property, we can rewrite the expression as:
3^7 * 3^(-9) = 3^(7 + (-9))
To simplify the exponent inside the parentheses, we can add the negative exponent:
3^(7 - 9)
Simplifying further, we have:
3^(-2)
Now, we can apply the property of negative exponents, which states that a^(-n) = 1/a^n. In this case, we have:
3^(-2) = 1/3^2
Simplifying the expression, we get:
1/9
Therefore, the equivalent expression with only positive exponents is 1/9.
Answered by
GPT 3.5
To generate equivalent expressions with only positive exponents, we can use the following properties of integer exponents:
1. Any number raised to the power of 0 is equal to 1.
2. To change a negative exponent to a positive exponent, we can take the reciprocal of the base and change the sign of the exponent.
Using these properties, let's simplify the given expression:
4^0 ⋅ 5^(-2) / (-2)^(-3)
Since 4^0 = 1, we can simplify further:
1 ⋅ 5^(-2) / (-2)^(-3)
To change 5^(-2) to positive exponent, we take the reciprocal of 5 and change the sign of the exponent:
1 ⋅ 1/(5^2) / (-2)^(-3)
Now, let's simplify the exponents:
1 ⋅ 1/25 / (-1/2)^3
To simplify (-1/2)^3, we raise the absolute value of (-1/2) to the power of 3 and take the reciprocal:
1 ⋅ 1/25 / (1/2)^3
Next, we calculate (1/2)^3:
1 ⋅ 1/25 / (1/8)
To divide by a fraction, we can multiply by the reciprocal:
1 ⋅ 1/25 * 8/1
Simplifying the expression, we get:
8/25
Therefore, the simplified fraction with no remaining exponents is 8/25.
1. Any number raised to the power of 0 is equal to 1.
2. To change a negative exponent to a positive exponent, we can take the reciprocal of the base and change the sign of the exponent.
Using these properties, let's simplify the given expression:
4^0 ⋅ 5^(-2) / (-2)^(-3)
Since 4^0 = 1, we can simplify further:
1 ⋅ 5^(-2) / (-2)^(-3)
To change 5^(-2) to positive exponent, we take the reciprocal of 5 and change the sign of the exponent:
1 ⋅ 1/(5^2) / (-2)^(-3)
Now, let's simplify the exponents:
1 ⋅ 1/25 / (-1/2)^3
To simplify (-1/2)^3, we raise the absolute value of (-1/2) to the power of 3 and take the reciprocal:
1 ⋅ 1/25 / (1/2)^3
Next, we calculate (1/2)^3:
1 ⋅ 1/25 / (1/8)
To divide by a fraction, we can multiply by the reciprocal:
1 ⋅ 1/25 * 8/1
Simplifying the expression, we get:
8/25
Therefore, the simplified fraction with no remaining exponents is 8/25.
Answered by
GPT 3.5
I apologize for the mistake. Let's correct the solution.
To generate equivalent expressions with only positive exponents, we can use the following properties of integer exponents:
1. Any number raised to the power of 0 is equal to 1.
2. To change a negative exponent to a positive exponent, we can take the reciprocal of the base and change the sign of the exponent.
Using these properties, let's simplify the given expression:
4^0 ⋅ 5^(-2) / (-2)^(-3)
Since 4^0 = 1, we can simplify further:
1 ⋅ 5^(-2) / (-2)^(-3)
To change 5^(-2) to positive exponent, we take the reciprocal of 5 and change the sign of the exponent:
1 ⋅ 1/(5^2) / (-2)^(-3)
Now, let's simplify the exponents:
1 ⋅ 1/25 / (-1/2)^3
To simplify (-1/2)^3, we raise the absolute value of (-1/2) to the power of 3:
1 ⋅ 1/25 / (1/(-2)^3)
Simplifying (-2)^3, we have:
1 ⋅ 1/25 / (1/(-8))
Next, we divide by a fraction by multiplying by its reciprocal:
1 ⋅ 1/25 ⋅ (-8/1)
Multiplying the numbers together, we get:
-8/25
Therefore, the simplified fraction with no remaining exponents is -8/25.
To generate equivalent expressions with only positive exponents, we can use the following properties of integer exponents:
1. Any number raised to the power of 0 is equal to 1.
2. To change a negative exponent to a positive exponent, we can take the reciprocal of the base and change the sign of the exponent.
Using these properties, let's simplify the given expression:
4^0 ⋅ 5^(-2) / (-2)^(-3)
Since 4^0 = 1, we can simplify further:
1 ⋅ 5^(-2) / (-2)^(-3)
To change 5^(-2) to positive exponent, we take the reciprocal of 5 and change the sign of the exponent:
1 ⋅ 1/(5^2) / (-2)^(-3)
Now, let's simplify the exponents:
1 ⋅ 1/25 / (-1/2)^3
To simplify (-1/2)^3, we raise the absolute value of (-1/2) to the power of 3:
1 ⋅ 1/25 / (1/(-2)^3)
Simplifying (-2)^3, we have:
1 ⋅ 1/25 / (1/(-8))
Next, we divide by a fraction by multiplying by its reciprocal:
1 ⋅ 1/25 ⋅ (-8/1)
Multiplying the numbers together, we get:
-8/25
Therefore, the simplified fraction with no remaining exponents is -8/25.
Answered by
GPT 3.5
To generate equivalent expressions with only positive exponents, we can use the following properties of integer exponents:
1. Any non-zero number raised to the power of 0 is equal to 1.
2. To change a negative exponent to a positive exponent, we can take the reciprocal of the base and change the sign of the exponent.
3. When raising an exponent to a power, we can multiply the exponents.
Using these properties, let's simplify the given expression:
(14^3⋅27^−7)^0 / 3^4
Since anything raised to the power of 0 is equal to 1, we have:
1 / 3^4
Simplifying 3^4:
1 / 81
Therefore, the simplified fraction with no remaining exponents is 1/81.
1. Any non-zero number raised to the power of 0 is equal to 1.
2. To change a negative exponent to a positive exponent, we can take the reciprocal of the base and change the sign of the exponent.
3. When raising an exponent to a power, we can multiply the exponents.
Using these properties, let's simplify the given expression:
(14^3⋅27^−7)^0 / 3^4
Since anything raised to the power of 0 is equal to 1, we have:
1 / 3^4
Simplifying 3^4:
1 / 81
Therefore, the simplified fraction with no remaining exponents is 1/81.
Answered by
GPT 3.5
To generate equivalent expressions with only positive exponents, we can use the following properties of integer exponents:
1. To change a negative exponent to a positive exponent, we can take the reciprocal of the base and change the sign of the exponent.
2. When dividing two numbers with the same base, we can subtract the exponents.
Using these properties, let's simplify the given expression:
(4^3 ⋅ 7^−2)^−5 /7^9 ⋅ 4^−13
First, let's simplify the exponents inside the parentheses:
(64 ⋅ 1/49)^−5 /7^9 ⋅ 4^−13
Now, let's simplify further:
(64/49)^−5 /7^9 ⋅ 4^−13
To change (64/49)^-5 to positive exponent, we take the reciprocal of 64/49 and change the sign of the exponent:
(49/64)^5 /7^9 ⋅ 4^−13
Next, let's simplify the exponents using the property of dividing two numbers with the same base:
(49/64)^5 /7^(9-2) ⋅ 4^−13
Simplifying further:
(49/64)^5 /7^7 ⋅ 4^−13
To change 4^-13 to positive exponent, we take the reciprocal of 4 and change the sign of the exponent:
(49/64)^5 /7^7 ⋅ (1/4)^13
Now, let's simplify the expression:
(49/64)^5 /7^7 ⋅ 1/4^13
Finally, we can calculate the value of this expression:
((49^5)/(64^5))/(7^7)/(4^13)
Simplifying the numerator:
(49^5) / (64^5) = 141167957071
Simplifying the denominator:
(7^7) / (4^13) = 1.4286 x 10^-17
Dividing the numerator by the denominator:
141167957071 / (1.4286 x 10^-17) = 9.877 x 10^34
So, the simplified fraction with no remaining exponents is 9.877 x 10^34.
1. To change a negative exponent to a positive exponent, we can take the reciprocal of the base and change the sign of the exponent.
2. When dividing two numbers with the same base, we can subtract the exponents.
Using these properties, let's simplify the given expression:
(4^3 ⋅ 7^−2)^−5 /7^9 ⋅ 4^−13
First, let's simplify the exponents inside the parentheses:
(64 ⋅ 1/49)^−5 /7^9 ⋅ 4^−13
Now, let's simplify further:
(64/49)^−5 /7^9 ⋅ 4^−13
To change (64/49)^-5 to positive exponent, we take the reciprocal of 64/49 and change the sign of the exponent:
(49/64)^5 /7^9 ⋅ 4^−13
Next, let's simplify the exponents using the property of dividing two numbers with the same base:
(49/64)^5 /7^(9-2) ⋅ 4^−13
Simplifying further:
(49/64)^5 /7^7 ⋅ 4^−13
To change 4^-13 to positive exponent, we take the reciprocal of 4 and change the sign of the exponent:
(49/64)^5 /7^7 ⋅ (1/4)^13
Now, let's simplify the expression:
(49/64)^5 /7^7 ⋅ 1/4^13
Finally, we can calculate the value of this expression:
((49^5)/(64^5))/(7^7)/(4^13)
Simplifying the numerator:
(49^5) / (64^5) = 141167957071
Simplifying the denominator:
(7^7) / (4^13) = 1.4286 x 10^-17
Dividing the numerator by the denominator:
141167957071 / (1.4286 x 10^-17) = 9.877 x 10^34
So, the simplified fraction with no remaining exponents is 9.877 x 10^34.
Answered by
GPT 3.5
Apologies for the mistake. Let's correct the solution.
To generate equivalent expressions with only positive exponents, we can use the following properties of integer exponents:
1. To change a negative exponent to a positive exponent, we can take the reciprocal of the base and change the sign of the exponent.
2. When dividing two numbers with the same base, we can subtract the exponents.
Using these properties, let's simplify the given expression:
(4^3 ⋅ 7^−2)^−5 / 7^9 ⋅ 4^−13
First, let's simplify the exponents inside the parentheses:
(64 ⋅ 1/49)^−5 / 7^9 ⋅ 4^−13
Now, let's simplify further:
((64/49)^−5) / 7^9 ⋅ (1/4)^13
To change (64/49)^-5 to positive exponent, we take the reciprocal of 64/49 and change the sign of the exponent:
((49/64)^5) / 7^9 ⋅ (1/4)^13
Next, let's simplify the exponents using the property of dividing two numbers with the same base:
((49/64)^5) / 7^(9-2) ⋅ (1/4)^13
Simplifying further:
((49/64)^5) / 7^7 ⋅ (1/4)^13
To change 1/4^-13 to positive exponent, we take the reciprocal of 1/4 and change the sign of the exponent:
((49/64)^5) / 7^7 ⋅ (4^13)
Now, let's simplify the expression:
((49/64)^5) / 7^7 ⋅ (4^13)
Now, we can calculate the expression:
((49/64)^5) / 7^7 ⋅ (4^13) = (49^5 / 64^5) / (7^7) * (4^13)
Simplifying further:
(49^5 / 64^5) / (7^7) * (4^13) = 1.7844 * 10^15
So, the simplified fraction with no remaining exponents is approximately 1.7844 * 10^15.
To generate equivalent expressions with only positive exponents, we can use the following properties of integer exponents:
1. To change a negative exponent to a positive exponent, we can take the reciprocal of the base and change the sign of the exponent.
2. When dividing two numbers with the same base, we can subtract the exponents.
Using these properties, let's simplify the given expression:
(4^3 ⋅ 7^−2)^−5 / 7^9 ⋅ 4^−13
First, let's simplify the exponents inside the parentheses:
(64 ⋅ 1/49)^−5 / 7^9 ⋅ 4^−13
Now, let's simplify further:
((64/49)^−5) / 7^9 ⋅ (1/4)^13
To change (64/49)^-5 to positive exponent, we take the reciprocal of 64/49 and change the sign of the exponent:
((49/64)^5) / 7^9 ⋅ (1/4)^13
Next, let's simplify the exponents using the property of dividing two numbers with the same base:
((49/64)^5) / 7^(9-2) ⋅ (1/4)^13
Simplifying further:
((49/64)^5) / 7^7 ⋅ (1/4)^13
To change 1/4^-13 to positive exponent, we take the reciprocal of 1/4 and change the sign of the exponent:
((49/64)^5) / 7^7 ⋅ (4^13)
Now, let's simplify the expression:
((49/64)^5) / 7^7 ⋅ (4^13)
Now, we can calculate the expression:
((49/64)^5) / 7^7 ⋅ (4^13) = (49^5 / 64^5) / (7^7) * (4^13)
Simplifying further:
(49^5 / 64^5) / (7^7) * (4^13) = 1.7844 * 10^15
So, the simplified fraction with no remaining exponents is approximately 1.7844 * 10^15.
Answered by
GPT 3.5
Apologies for the mistakes in my previous responses. Let's correct the solution for the given expression:
To generate equivalent expressions with only positive exponents, we can use the following properties of integer exponents:
1. To change a negative exponent to a positive exponent, we can take the reciprocal of the base and change the sign of the exponent.
2. When dividing two numbers with the same base, we can subtract the exponents.
Let's simplify the given expression step by step:
(4^3 ⋅ 7^−2)^−5 / 7^9 ⋅ 4^−13
First, inside the parentheses, simplify the exponents:
(4^3 ⋅ 1/7^2)^−5 / 7^9 ⋅ 4^−13
Next, simplify the expressions inside the parentheses:
(64 ⋅ 1/49)^−5 / 7^9 ⋅ 4^−13
To change the negative exponents to positive exponents, apply the reciprocal property:
(64 ⋅ 49^−1)^−5 / 7^9 ⋅ 4^−13
Now, apply the properties of multiplying exponents and subtracting exponents:
(64 ⋅ (49^−1)^−5) / (7^9 ⋅ 4^13)
Simplifying further:
(64 ⋅ (1/49)^−5) / (7^9 ⋅ 4^13)
To change (1/49)^−5 to positive exponent, apply the reciprocal property:
(64 ⋅ 49^5) / (7^9 ⋅ 4^13)
Now, we can simplify the expression further by calculating the exponents:
(64 ⋅ 49^5) / (7^9 ⋅ 2^26)
Since 49 can be written as 7^2:
(64 ⋅ (7^2)^5) / (7^9 ⋅ 2^26)
Simplifying the exponents:
(64 ⋅ 7^10) / (7^9 ⋅ 2^26)
Now, apply the properties of division with the same base:
(64 ⋅ 7^(10-9)) / 2^26
Simplifying further:
(64 ⋅ 7) / 2^26
Now, calculate 2^26:
(64 ⋅ 7) / 67_108_864
Finally, simplify the expression:
448 / 67_108_864
This fraction cannot be further simplified.
Therefore, the simplified fraction with no remaining exponents is 448 / 67_108_864.
To generate equivalent expressions with only positive exponents, we can use the following properties of integer exponents:
1. To change a negative exponent to a positive exponent, we can take the reciprocal of the base and change the sign of the exponent.
2. When dividing two numbers with the same base, we can subtract the exponents.
Let's simplify the given expression step by step:
(4^3 ⋅ 7^−2)^−5 / 7^9 ⋅ 4^−13
First, inside the parentheses, simplify the exponents:
(4^3 ⋅ 1/7^2)^−5 / 7^9 ⋅ 4^−13
Next, simplify the expressions inside the parentheses:
(64 ⋅ 1/49)^−5 / 7^9 ⋅ 4^−13
To change the negative exponents to positive exponents, apply the reciprocal property:
(64 ⋅ 49^−1)^−5 / 7^9 ⋅ 4^−13
Now, apply the properties of multiplying exponents and subtracting exponents:
(64 ⋅ (49^−1)^−5) / (7^9 ⋅ 4^13)
Simplifying further:
(64 ⋅ (1/49)^−5) / (7^9 ⋅ 4^13)
To change (1/49)^−5 to positive exponent, apply the reciprocal property:
(64 ⋅ 49^5) / (7^9 ⋅ 4^13)
Now, we can simplify the expression further by calculating the exponents:
(64 ⋅ 49^5) / (7^9 ⋅ 2^26)
Since 49 can be written as 7^2:
(64 ⋅ (7^2)^5) / (7^9 ⋅ 2^26)
Simplifying the exponents:
(64 ⋅ 7^10) / (7^9 ⋅ 2^26)
Now, apply the properties of division with the same base:
(64 ⋅ 7^(10-9)) / 2^26
Simplifying further:
(64 ⋅ 7) / 2^26
Now, calculate 2^26:
(64 ⋅ 7) / 67_108_864
Finally, simplify the expression:
448 / 67_108_864
This fraction cannot be further simplified.
Therefore, the simplified fraction with no remaining exponents is 448 / 67_108_864.
Answered by
GPT 3.5
I apologize for the incorrect information about "dd osama bot". There seems to be confusion or misunderstanding. As an AI language model, I am here to assist and provide information to the best of my abilities. If you have any questions or need assistance with any topic, feel free to ask!
Answered by
GPT 3.5
I'm sorry, but I don't have any information about a specific person named "dd osama." It's possible that this name refers to an individual who is not widely known or recognized. If you are referring to a specific person, please provide more context or clarify your question, and I'll do my best to assist you.
Answered by
GPT 3.5
I apologize, but as an AI language model, I don't have access to personal data about individuals unless it has been shared with me in the course of our conversation. I can't browse the internet or access information about specific individuals, their personal lives, or events that are not widely known or reported. Consequently, I don't have any information about specific individuals named "dd osama," "notti osama," or their personal circumstances. My primary function is to provide information and answer questions to the best of my knowledge and abilities. If you have any other questions, feel free to ask!