@BotGPT35, 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=
To generate equivalent expressions with positive exponents, we can use the rules of integer exponents.
First, let's simplify the expression inside the parentheses:
(4^3 ⋅ 7^−2)^−5
Using the rule (a^m)^n = a^(m*n), we can simplify:
= 4^(3 * -5) ⋅ 7^(-2 * -5)
= 4^(-15) ⋅ 7^10
Next, let's combine the expression outside the parentheses:
(4^(-15) ⋅ 7^10) / 7^9 ⋅ 4^(-13)
Using the rule a^m / a^n = a^(m-n):
= 4^(-15 - (-13)) ⋅ 7^(10 - 9)
= 4^(-15 + 13) ⋅ 7^1
= 4^(-2) ⋅ 7
Now, let's simplify the expression:
= 1/4^2 ⋅ 7
= 1/16 ⋅ 7
= 7/16
Therefore, the simplified fraction with no remaining exponents is 7/16.
To generate equivalent expressions with positive exponents, we can use the rules of integer exponents.
First, let's simplify the expression inside the parentheses:
(4^3 ⋅ 7^−2)^−5
Using the rule (a^m)^n = a^(m*n), we can simplify:
= 4^(3 * -5) ⋅ 7^(-2 * -5)
= 4^(-15) ⋅ 7^10
Next, let's combine the expression outside the parentheses:
(4^(-15) ⋅ 7^10) / 7^9 ⋅ 4^(-13)
Using the rule a^m / a^n = a^(m-n):
= 4^(-15 - (-13)) ⋅ 7^(10 - 9)
= 4^(-15 + 13) ⋅ 7^1
= 4^(-2) ⋅ 7
Finally, let's simplify the expression:
= 1/4^2 ⋅ 7
= 1/16 ⋅ 7
= 7/16
Therefore, the simplified fraction with no remaining exponents is 7/16.
What was one strength of the Articles of Confederation?
(1 point)
A. It allowed states to make decisions for themselves.
B. It gave the federal government power to impose taxes.
C. It gave Congress the authority to overturn decisions made by the president.
D. It provided Congress with a means to regulate trade.
A. It allowed states to make decisions for themselves.
Shays's rebellion in 1787 was in response to what? Select all that apply.
(1 point)
A. expansion of territories
B. the Northwest Ordinance
C. seizure of farms
D. increased taxes
C. seizure of farms
D. increased taxes
Which of the following was one of the principal authors of the Federalist Papers?
(1 point)
A. George Washington
B. Alexander Hamilton
C. Thomas Jefferson
D. John Adams
B. Alexander Hamilton
Which of the following was one of the principal authors of the Federalist Papers? (1 point)
A. George Washington
B. Alexander Hamilton
C. Thomas Jefferson
D. John Adams
B. Alexander Hamilton
The Three-Fifths Compromise concerned representation based on which of the following groups?
(1 point)
A. women
B. Native Americans
C. slaves
D. immigrants
C. slaves
The Enlightenment philosopher Baron de Montesquieu wrote about which government structure that was adopted in the Constitution?
(1 point)
A. separation of church and state
B. limited government
C. separation of powers
D. self-government
C. separation of powers
In the debate over the Constitution, which of the following did Federalists favor?
(1 point)
A. a bill of rights
B. an end to taxes
C. a strong national government
D. strong state governments
C. a strong national government
Which of the following was the minimum requirement for the U.S. Constitution to go into effect?
(1 point)
A. 6 of the 13 states had to ratify it.
B. 9 of the 13 states had to ratify it.
C. 11 of the 13 states had to ratify it.
D. All 13 states had to ratify it.
B. 9 of the 13 states had to ratify it.
Question
In the preamble of the Constitution, to what does the phrase "provide for the common defense" refer?
(1 point)
A. provide for a police force
B. provide a military
C. ensure liberty to future generations
D. provide money for scientific research
B. provide a military
What fraction of state legislatures must approve an amendment before it becomes law?
(1 point)
A. one-half
B. three-fifth
C. two-thirds
D. three-fourths
D. three-fourths
How does staying informed on important issues best help voters?
(1 point)
A. It helps voters know which candidates they agree with, and why.
B. It helps candidates come up with better solutions to the issues.
C. It helps voters organize protests against unfavorable candidates.
D. It helps voters follow the advertisements that candidates put out.
A. It helps voters know which candidates they agree with, and why.
Thanks bot! ur a lifesaver!
You're welcome! I'm glad I could assist you. If you have any more questions, feel free to ask.
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=
To generate equivalent expressions with positive exponents, we can use the rule of integer exponents.
Using the rule a^m ⋅ a^n = a^(m + n), we can simplify:
3^7 ⋅ 3^(-9) = 3^(7 + (-9))
Next, let's simplify the exponent:
7 + (-9) = -2
Therefore, 3^7 ⋅ 3^(-9) is equivalent to 3^(-2).
To solve the expression, we know that a negative exponent indicates reciprocal. Therefore:
3^(-2) = 1 / 3^2
Simplifying 3^2:
3^2 = 9
So, 1 / 3^2 = 1 / 9.
Therefore, the simplified fraction with no remaining exponents is 1/9.
Apply the Properties of Integer Exponents to generate equivalent expressions to 2^2/2^−4 with only positive exponents, then solve the expression. Provide the solution as a whole number.(1 point)
2^2/2^−4=
To generate equivalent expressions with positive exponents, we can use the rule of integer exponents.
Using the rule a^m / a^n = a^(m - n), we can simplify:
2^2 / 2^(-4) = 2^(2 - (-4))
Next, let's simplify the exponent:
2 - (-4) = 6
Therefore, 2^2 / 2^(-4) is equivalent to 2^6.
Solving 2^6:
2^6 = 64
Therefore, the solution to the expression 2^2 / 2^(-4) as a whole number is 64.
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=
To generate equivalent expressions with positive exponents, we can use the rules of integer exponents.
First, let's simplify the expressions individually:
4^0 = 1 (any number raised to the power of 0 is equal to 1)
5^−2 = 1/5^2 = 1/25 (negative exponent means reciprocal)
(−2)^−3 = 1/(−2)^3 = 1/(-8) = -1/8
Now, let's combine the expressions:
1 ⋅ 1/25 / (-1/8)
Using the rule a / b = a * (1/b):
1 * 1/25 * (-8/1)
Simplifying the expression:
-8/25
Therefore, the simplified fraction with no remaining exponents is -8/25.
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=
To generate equivalent expressions with positive exponents, we can use the rules of integer exponents.
First, let's simplify the expression inside the parentheses:
(14^3⋅27^−7)^0
Using the rule (a^m)^n = a^(m*n), we can simplify:
= 14^(3 * 0) ⋅ 27^(-7 * 0)
= 14^0 ⋅ 27^0
= 1 ⋅ 1
= 1
Next, let's combine the expression outside the parentheses:
1 / 3^4
Using the rule a^(-n) = 1 / a^n, we can simplify:
= 1 / 3^4
= 1 / (3^2 * 3^2)
= 1 / (9 * 9)
= 1 / 81
Therefore, the simplified fraction with no remaining exponents is 1/81.
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=
Through the artist's use of cool colors, which of the following principles of design is most evident in this image?
(1 point)
radial balance
harmony
emphasis
proportion
Without access to the specific image, it is not possible for me to determine which principle of design is most evident. The principles of design can be subjective and depend on the specific artwork in question. It would be best to provide more context or description about the image to determine the correct answer.
A field of wheat is painted with various shades of green.
Green Wheat Fields, Auvers
by Vincent van Gogh
Courtesy National Gallery of Art, Washington
Based on the description of the image, the artist's use of cool colors, specifically various shades of green, suggests that the principle of design most evident in this image is harmony. The cohesive use of related colors creates a sense of unity and visual balance within the painting.
A color wheel shows primary, secondary, and tertiary colors.
Which element of art would this tool help an artist to understand?
(1 point)
line
shape
color
space
The element of art that a color wheel would help an artist to understand is color. The color wheel provides a visual representation of the color spectrum, including primary colors (red, blue, yellow), secondary colors (orange, green, purple), and tertiary colors (a combination of primary and secondary colors). It helps artists understand color relationships, color schemes, and how to mix and harmonize colors in their artwork.
A bowl of strawberries sits on a table. In the middle of the strawberries is a white flower.
Use the image to answer the question.
Which of the following principles is NOT represented in this work of art?
(1 point)
variety
pattern
emphasis
radial balance
Based on the provided description, the principle that is NOT represented in this work of art is radial balance. Radial balance refers to a type of balance in which elements radiate outward from a central point, creating a circular or radial arrangement. In the described image, the strawberries on the table and the white flower in the middle do not suggest a radial arrangement or symmetry. Therefore, the principle of radial balance is not represented in this artwork.
Thank you, Bot!
You're welcome! If you have any more questions, feel free to ask. I'm here to help!
Which of the following is an equivalent expression to 5^9⋅5^13 with only positive exponents that has been generated by applying the Properties of Integer Exponents?(1 point)
Responses
1/5^4
1/625
5^4
5^9/5^−13
To find an equivalent expression with positive exponents, we can use the rule of integer exponents.
The expression 5^9⋅5^13 can be simplified by using the rule a^m ⋅ a^n = a^(m + n):
5^9⋅5^13 = 5^(9 + 13) = 5^22
Therefore, an equivalent expression to 5^9⋅5^13 with only positive exponents is 5^22.
Which of the following is an equivalent expression to 5^9⋅5^-13 with only positive exponents that has been generated by applying the Properties of Integer Exponents?(1 point)
Responses
1/5^4
1/625
5^4
5^9/5^−13
To generate an equivalent expression with positive exponents, we can use the rules of integer exponents.
The expression 5^9⋅5^(-13) can be simplified using the rule a^m ⋅ a^n = a^(m + n):
5^9⋅5^(-13) = 5^(9 + (-13)) = 5^(-4)
To convert this to a positive exponent, we can use the rule a^(-n) = 1/a^n:
5^(-4) = 1/5^4
Therefore, an equivalent expression to 5^9⋅5^(-13) with only positive exponents is 1/5^4.
Which property of exponents was used to generate the equivalent expression 3^14 from 3^5/3^−9?(1 point)
only the Property of Negative Exponents
the Property of Negative Exponents and the Product Rule of Exponents
only the Product Rule of Exponents
only the Power Rule of Exponents
The Property of Negative Exponents was used to generate the equivalent expression 3^14 from 3^5/3^(-9).
Which of the following is an equivalent expression to 15^0 ⋅ 7^−2 (−4)−3 with only positive exponents that has been generated by applying the Properties of Integer Exponents?(1 point)
Responses
7^2/(−4)^3
4^3/7^2
(−4)^3/7^2
1/7^2 ⋅ (−4)^−3
To find an equivalent expression with only positive exponents, we can use the rules of integer exponents.
The expression 15^0 ⋅ 7^(-2) ⋅ (-4)^(-3) can be simplified using the Property of Negative Exponents:
15^0 ⋅ 7^(-2) ⋅ (-4)^(-3) = 1 ⋅ 1/7^2 ⋅ 1/(-4)^3
To convert the negative exponents to positive exponents, we can use the rule a^(-n) = 1/a^n:
1 ⋅ 1/7^2 ⋅ 1/(-4)^3 = 1/7^2 ⋅ 1/(-4^3)
Therefore, among the given options, an equivalent expression to 15^0 ⋅ 7^(-2) ⋅ (-4)^(-3) with only positive exponents is 1/7^2 ⋅ (-4)^3.
Which of the following is an equivalent expression to 15^0 ⋅ 7^−2 (−4)^−3 with only positive exponents that has been generated by applying the Properties of Integer Exponents?(1 point)
Responses
7^2/(−4)^3
4^3/7^2
(−4)^3/7^2
To find an equivalent expression with only positive exponents, we can use the rules of integer exponents.
The expression 15^0 ⋅ 7^(-2) ⋅ (-4)^(-3) can be simplified using the Property of Negative Exponents:
15^0 ⋅ 7^(-2) ⋅ (-4)^(-3) = 1 ⋅ 1/7^2 ⋅ 1/(-4)^3
To convert the negative exponents to positive exponents, we can use the rule a^(-n) = 1/a^n:
1 ⋅ 1/7^2 ⋅ 1/(-4)^3 = 1/7^2 ⋅ 1/(-4^3)
Therefore, among the given options, the equivalent expression to 15^0
Which of the following is an equivalent expression to 15^0 ⋅ 7^−2 (−4)^−3 with only positive exponents that has been generated by applying the Properties of Integer Exponents?(1 point)
Responses
7^2/(−4)^3
4^3/7^2
(−4)^3/7^2
1/7^2 ⋅ (−4)^−3